regularity for p harmonic equations with right hand side in orlicz zygmund classes abstract we establish regularity results for solutions of some degenerate elliptic pdes with right hand side in a suitable orlicz zygmund class the nonnegative function which measures the degree of degeneracy of the ellipticity bounds is assumed to be exponentially integrable we find that the scale of improved regularity is logarithmic and we indicate its exact dependence on the degree of the degeneracy of the problem

tdgl and mkdv equations for jamming transition in the lattice models of traffic abstract the lattice models of traffic are proposed to describe the jamming transition in traffic flow on a highway in terms of thermodynamic terminology of phase transitions and critical phenomena they are the lattice versions of the hydrodynamic model of traffic two lattice models are presented one is described by the differential difference equation where time is a continuous variable and space is a discrete variable and the other is the difference equation in which both time and space variables are discrete we apply the linear stability theory and the nonlinear analysis to the lattice models it is shown that the time dependent ginzburg landau tdgl equation is derived to describe the traffic flow near the critical point a thermodynamic theory is formulated for describing the phase transitions and critical phenomena it is also shown that the perturbed modified korteweg de vries mkdv equation is derived to describe the traffic jam

new maximal functions and multiple weights for the multilinear calderon zygmund theory a multi sub linear maximal operator that acts on the product of m lebesgue spaces and is smaller than the m fold product of the hardy littlewood maximal function is studied the operator is used to obtain a precise control on multilinear singular integral operators of calderon zygmund type and to build a theory of weights adapted to the multilinear setting a natural variant of the operator which is useful to control certain commutators of multilinear calderon zygmund operators with bmo functions is then considered the optimal range of strong type estimates a sharp end point estimate and weighted norm inequalities involving both the classical muckenhoupt weights and the new multilinear ones are also obtained for the commutators

bi sobolev mappings and elliptic equations in the plane abstract suppose that f u v is a homeomorphism in the plane of the sobolev class w loc 1 1 such that its inverse is of the same sobolev class we prove that u and v have the same set of critical points as an application we show that u and v are distributional solutions to the same non trivial degenerate elliptic equation in divergence form we study similar properties also in higher dimensions

calderon zygmund estimates and non uniformly elliptic operators abstract we consider a class of non uniformly nonlinear elliptic equations whose model is given by div d u p 2 d u a x d u q 2 d u div f p 2 f a x f q 2 f where p q and a x 0 and establish the related nonlinear calderon zygmund theory in particular we provide sharp conditions under which the natural and optimal calderon zygmund type result f p a x f q l loc d u p a x d u q l loc holds for every 1 these problems naturally emerge as euler lagrange equations of some variational integrals introduced and studied by marcellini 41 and zhikov 53 in the framework of homogenisation and lavrentiev phenomenon

very weak solutions of degenerate parabolic systems with non standard p x t growth abstract we study higher integrability of very weak solutions to certain degenerate parabolic systems whose model is the parabolic p x t laplacian system t u div d u p x t 2 d u div f p x t 2 f under natural assumptions on the exponent function p 0 t 2 we prove that any very weak solution u 0 t r n with d u p 1 e l 1 belongs to the natural energy space i e d u p l loc 1 provided e 0 is small enough

analysis of car following model considering driver s physical delay in sensing headway abstract an extended car following model is proposed by taking into account the delay of the driver s response in sensing headway the stability condition of this model is obtained by using the linear stability theory the results show that the stability region decreases when the driver s physical delay in sensing headway increases the kdv equation and mkdv equation near the neutral stability line and the critical point are respectively derived by applying the reductive perturbation method the traffic jams could be thus described by soliton solution and kink antikink soliton solution for the kdv equation and mkdv equation respectively the numerical results in the form of the space time evolution of headway show that the stabilization effect is weakened when the driver s physical delay increases it confirms the fact that the delay of driver s response in sensing headway plays an important role in jamming transition and the numerical results are in good agreement with the theoretical analysis

existence and uniqueness for nonlinear elliptic equations with lower order terms abstract we study the nonlinear dirichlet problem for the elliptic equation div a x u b x u div f in a regular domain r n n 2 u 0 on in hypothesis of lipschitz continuity and strong monotonicity of a we assume that the lower order term b x s verify b x s b x t e x s t for a e x and for any s t r where e is a non negative function in the lorentz space l n q n q without any control on the norm of e with f l p p 1 and q we obtain existence and uniqueness result for distributional solutions u w 1 p whenever p is close to two for q uniqueness results are obtained the main difficulty to solve the problem is due to noncoercivity of the vector field a x s a x b x s moreover no classical structure conditions are satisfied

on the operator l f f log f abstract the present note deals with the operator l h 1 r n d r n which takes a given element f of the hardy space to the function f log f in general this function need not be locally integrable nevertheless due to peculiar cancellations of large positive and negative terms in the integral f log f with c 0 r n we are able to give meaning to f log f as a schwartz distribution we find several alternatives for this interpretation of f log f

kdv and kink antikink solitons in car following models abstract the jams in the congested traffic are related with various density waves which might be governed by the nonlinear wave equations such as the korteweg de vries kdv equation the burgers equation and the modified korteweg de vries mkdv equation three different versions of optimal velocity models are examined the stability conditions of the models are obtained by using the linear stability theory the kdv equation near the neutral stability line and the mkdv equation around the critical point are derived by applying the reductive perturbation method respectively the traffic jams could be thus described by the kdv and kink antikink soliton solutions for the two kinds of equations the general solutions are given for which can lead to specific solutions in previous work moreover they are applied to solve a new model the full velocity difference model and the corresponding kdv and kink antikink soliton solutions could be quickly obtained which demonstrates the general solutions presented herein are useful

generalized area operators on hardy spaces abstract we show that if 0 0 and 1 p 0 then the operatorgfmaps the hardy sobolev spacehp intolp d if and only if the functiong d 1 z belongs to the morrey spacelp 1 p in casep 1 this condition is equivalent to the condition that t i c i 1 for all arcsicontained in the circle wheret i is the tent overicontained in the unit disk

integral estimates for null lagrangians sobolev spaces of differential forms are studied lp projections onto exact forms are introduced as a tool to obtain integral estimates for null lagrangians new results on compensated compactness are given and mean coercive variational integrals are found existence of minima of certain mean coercive functionals is established

the theoretical analysis of the lattice hydrodynamic models for traffic flow theory abstract the lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model but also connected with the microscopic car following model closely the modified korteweg de vries mkdv equation related to the density wave in a congested traffic region has been derived near the critical point since nagatani first proposed it but the korteweg de vries kdv equation near the neutral stability line has not been studied which has been investigated in detail for the car following model we devote ourselves to obtaining the kdv equation from the original lattice hydrodynamic models and the kdv soliton solution to describe the traffic jam especially we obtain the general soliton solution of the kdv equation and the mkdv equation we review several lattice hydrodynamic models which were proposed recently we compare the modified models and carry out some analysis numerical simulations are conducted to demonstrate the nonlinear analysis results

local regularity for solutions of anisotropic obstacle problems abstract this paper deals with anisotropic obstacle problems for the a harmonic equation div a x u x 0 a local regularity result is given under suitable assumptions

nonlinear cauchy riemann operators in ℝⁿ this paper has arisen from an effort to provide a comprehensive and unifying development of the l p theory of quasiconformal mappings in r n the governing equations for these mappings form nonlinear differential systems of the first order analogous in many respects to the cauchy riemann equations in the complex plane this approach demands that one must work out certain variational integrals involving the jacobian determinant guided by such integrals we introduce two nonlinear differential operators denoted by d and d which act on weakly differentiable deformations f r n of a domain c r n solutions to the so called cauchy riemann equations d f 0 and d f 0 are simply conformal deformations preserving and reversing orientation respectively these operators though genuinely nonlinear possess the important feature of being rank one convex among the many desirable properties we give the fundamental l p estimate d f p a p n d f p in quest of the best constant a p n we are faced with fascinating problems regarding quasiconvexity of some related variational functionals applications to quasiconformal mappings are indicated

existence results for some nonuniformly elliptic equations with irregular data abstract in this paper we prove the existence of solutions of some nonlinear elliptic equations with degenerate coercivity of the type formula when the datum f belongs to the space lr where r 2 and 0 1

kink soliton characterizing traffic congestion we study traffic congestion by analyzing a one dimensional traffic flow model developing an asymptotic method to investigate the long time behavior near a critical point we derive the modified korteweg de vries mkdv equation as the lowest order model there is an infinite number of kink solitons to the mkdv equation while it has been found by numerical simulations that the kink pattern arising in traffic congestion is uniquely determined irrespective of initial conditions in order to resolve this selection problem we consider higher order corrections to the mkdv equation and find that there is a kink soliton that can deform continuously with the perturbation represented by the addition of these corrections with numerical confirmation we show that this continuously deformable kink soliton characterizes traffic congestion we also discuss the relationship between traffic congestion and the slugging phenomenon in granular flow

the maximum principle of alexandrov for very weak solutions abstract we extend the classical maximal principle of alexandrov to very weak solutions of the elliptic equation i j 1 n a i j x 2 u x i x j f

global higher integrability for the gradient of very weak solutions of a class of nonlinear elliptic systems abstract the global higher integrability for the gradient of very weak solutions of nonlinear elliptic systems div a x u du b x u du u u 0 w 0 1 r is obtained where is a bounded domain in rn with a lipschitz boundary max 1 p 1

intermittent unstable structures induced by incessant constant disturbances in the full velocity difference car following model abstract in this paper we study traffic flow patterns induced by incessant constant disturbances in the full velocity difference car following model it is found that intermittent unstable structures may occur in the convectively unstable traffic flow under certain situations a phenomenological explanation of the phenomenon is given the incessant constant disturbances mainly function to maintain the stationary oscillating structure while the stationary oscillating structure is not always stable the intermittent instability of it leads to the intermittent unstable structures the similarity of the stationary oscillating structure to the transition layer in the local cluster effect is pointed out the dependence of the phenomenon on the headway of the initially uniform traffic the safety distance x c the sensitivity parameters and and the noise term is also investigated

scaling behaviour in discrete traffic models we investigate the noisy discrete single lane highway traffic model proposed by nagel and schreckenberg 1992 and demonstrate by computer simulations that as a function of the car density there is a dynamical transition from laminar flow to jammed traffic in the system related to the divergence of the relaxation time of average car velocity the critical density is close to the position of the maximum in the fundamental diagram we give estimates of the critical exponents related to this jamming transition the critical density of the geometrical 1 1 dimensional percolation transition of jammed regions can be rather far from the jamming point depending on the strength of the noise which indicates that cooperativity leading to the jamming transition can be long range in character

jamming transition in two dimensional pedestrian traffic abstract jamming transitions of pedestrian traffic are investigated under the periodic boundary condition on the square lattice by the use of the lattice gas model of biased random walkers without the back step the two cases are presented the one with two types of walkers and the other with four types of walkers in the two types of walkers the first is the random walker going to the right and the second is the random walker going up in the four types of walkers the first second third and fourth are respectively the random walkers going to the right left up and down it is found that the dynamical jamming transitions occur at the critical densities the transition points do not depend on the system size for large system but depend strongly on the strength of drift the jamming transitions are compared with that obtained by the cellular automaton model of car traffic

t minima and application to the convergence of some integral functionals with infinite energy minima abstract we consider integral functionals j as in 1 we study the calderon zygmund theory for infinite energy minima u t minima of j and the stability of the t minima with respect to the convergence in 22 with v w 0 1 p

exact solutions for a discrete system arising in traffic flow this paper concerns wave propagation in a discrete nonlinear system of equations proposed and studied by g f newell as a model for car following in traffic flow in particular newell found exact solutions for shock waves and related phenomena here exact solutions representing periodic waves and solitary waves are obtained the method relates travelling wave solutions to the toda and kac van moerbeke discrete systems in this and other ways much of the interest is in the general phenomena possible in discrete systems here including also a time lag rather than in just the specific traffic flow setting

the korteweg de vries soliton in the lattice hydrodynamic model abstract the lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model but is also closely connected with the microscopic car following model the modified korteweg de vries mkdv equation about the density wave in congested traffic has been derived near the critical point since nagatani first proposed it but the korteweg de vries kdv equation near the neutral stability line has not been studied which has been investigated in detail in the car following model so we devote ourselves to obtaining the kdv equation from the lattice hydrodynamic model and obtaining the kdv soliton solution describing the traffic jam numerical simulation is conducted to demonstrate the nonlinear analysis result

modified kdv equation for jamming transition in the continuum models of traffic abstract continuum models of traffic are proposed to describe the jamming transition in traffic flow on a highway they are the simplified versions of the hydrodynamic model of traffic two continuum models are presented one is described by the partial differential equations and the other is the discrete lattice version the linear stability theory and the nonlinear analysis are applied to the continuum models the modified korteweg de vries equation kdv near the critical point is derived using the reduction perturbation method it is shown that the jamming transition and the density wave in the congested traffic flow are described by the modified kdv equation the solutions of the kdv equations obtained from the two models are compared with that of the optimal velocity model car following model

on very weak solutions to a class of double obstacle problems abstract we prove the uniqueness of very weak solutions by hodge decomposition and obtain the existence by an approximation argument moreover we prove that the solution quasiminimizes the r dirichlet integral in k r and finally the stability of very weak solutions is established for varying obstacle functions

phase transition in a difference equation model of traffic flow a difference equation is presented to describe traffic flow on a highway the difference equation model is derived from the optimal velocity models formulated in terms of the differential equations it is compared with the differential equation models we investigate phase transitions among the freely moving phase the coexisting phase in which jams appear and the uniform congested phase the linear stability theory is applied and the neutral stability line is obtained we find the critical point below which no jams appear to derive the modified korteweg de vries equation near the critical point we apply the reductive perturbation method we also compare the nonlinear analysis result with that of the optimal velocity model it is shown that the critical point and the amplitude of the jam are different from those of the optimal velocity model

developments and perspectives in nonlinear potential theory abstract nonlinear potential theory aims at replicating the classical linear potential theory when nonlinear equations are considered in recent years there has been a substantial development of this subject mostly linked to the possibility of proving pointwise estimates for solutions to nonlinear equations via linear and nonlinear potentials here we give a brief account of such developments and outline the connections with different fields

traffic jams granular flow and soliton selection the flow of traffic on a long section of road without entrances or exits can be modeled by continuum equations similar to those describing fluid flow in a certain range of traffic density steady flow becomes unstable against the growth of a cluster or phantom traffic jam which moves at a slower speed than the otherwise homogeneous flow we show that near the onset of this instability traffic flow is described by a perturbed korteweg de vries kdv equation the traffic jam can be identified with a soliton solution of the kdv equation the perturbation terms select a unique member of the continuous family of kdv solitons these results may also apply to the dynamics of granular relaxation

jamming transitions and the modified korteweg de vries equation in a two lane traffic flow abstract the two lattice models are presented to simulate the traffic flow on a two lane highway they are the lattice versions of the hydrodynamic model of traffic the one model a is described by the differential difference equation where time is a continuous variable and space is a discrete variable and the other model b is the difference equation in which both time and space variables are discrete the jamming transitions among the freely moving phase the coexisting phase and the uniform congested phase are studied by using the nonlinear analysis and the computer simulation the modified korteweg de vries mkdv equations are derived from the lattice models near the critical point the traffic jam is described by a kink antikink solution obtained from the mkdv equation it is found that the critical point the coexisting curve and the neutral stability line decrease with increasing the rate of lane changing also the computer simulation is performed for the model b it is shown that the coexisting curves obtained from the mkdv equation are consistent with the simulation result

solitons and kinks in a general car following model we study a general car following model of traffic flow on an infinitely long single lane road which assumes that a car s acceleration depends on time delayed values of its own speed the headway between it and the car ahead and the rate of change of headway but makes minimal assumptions about the functional form of that dependence we present a detailed characterization of the onset of linear instability in particular we find a specific limit on the delay time below which the marginal wave number at the onset of instability is zero and another specific limit on the delay time above which steady flow is always unstable crucially the threshold of absolute stability generally does not coincide with an inflection point of the steady state velocity function when the marginal perturbation at onset has wave number 0 we show that burgers and korteweg de vries kdv equations can be derived under the usual assumptions and that corrections to the kdv equation select a single member of the one parameter set of its one soliton solutions by driving a slow evolution of the soliton parameter while in previous models this selected soliton has always marked the threshold of a finite amplitude instability of linearly stable steady flow we find that it can alternatively be a stable small amplitude jam that occurs when steady flow is linearly unstable the model reduces to the usual modified korteweg de vries mkdv equation only in the special situation that the threshold of absolute stability coincides with an inflection point of the steady state velocity function in general near the threshold of absolute stability the model reduces instead to a kdv equation in the regime of small solitons while near an inflection point it reduces to a hayakawa nakanishi equation like the mkdv equation the hayakawa nakanishi equation admits a continuous family of kink solutions and the selection criterion arising from the corrections to this equation can be written down explicitly language en

bergman projections and operators on hardy spaces we show that toeplitz like operators of the formtsuf ps uf wherepsis a weighted bergman projection are bounded on the hardy spaceshp for 1 p for certain symbols udefined on the unit disk in particular tsuis bounded ifuis of the formu h g wherehis a bounded harmonic function andg is the green potential of a borel measure satisfying the condition that 1 z d z is a carleson measure ifuis of the formu h g where is a positive measure then these two conditions are also necessary thattsube bounded onhp we also consider the cases 0 p 1

gas kinetic derivation of navier stokes like traffic equations macroscopic traffic models have recently been severely criticized to base on lax analogies only and to have a number of deficiencies therefore this paper shows how to construct a logically consistent fluid dynamic traffic model from basic laws for the acceleration and interaction of vehicles these considerations lead to the gas kinetic traffic equation of paveri fontana its stationary and spatially homogeneous solution implies equilibrium relations for the fundamental diagram the variance density relation and other quantities which are partly difficult to determine empirically paveri fontana s traffic equation allows the derivation of macroscopic moment equations which build a system of non closed equations this system can be closed by the well proved method of chapman and enskog which leads to euler like traffic equations in zeroth order approximation and to navier stokes like traffic equations in first order approximation the latter are finally corrected for the finite space requirements of vehicles it is shown that the resulting model is able to withstand the above mentioned criticism

solvable optimal velocity models and asymptotic trajectory in the optimal velocity model proposed as a new version of car following model it has been found that a congested flow is generated spontaneously from a homogeneous flow for a certain range of the traffic density a well established congested flow obtained in a numerical simulation shows a remarkable repetitive property such that the velocity of a vehicle evolves exactly in the same way as that of its preceding one except a time delay t this leads to a global pattern formation in time development of vehicles motion and gives rise to a closed trajectory on delta x v headway velocity plane connecting congested and free flow points to obtain the closed trajectory analytically we propose a new approach to the pattern formation which makes it possible to reduce the coupled car following equations to a single difference differential equation rondo equation to demonstrate our approach we employ a class of linear models which are exactly solvable we also introduce the concept of asymptotic trajectory to determine t and v b the backward velocity of the pattern the global parameters associated with vehicles collective motion in a congested flow in terms of parameters such as the sensitivity a which appeared in the original coupled equations

density waves in the full velocity difference model density waves are investigated in the full velocity difference model fvdm analytically and numerically by the use of nonlinear analysis the burgers korteweg de vries kdv and modified kdv equations are derived for the triangular shock wave the soliton wave and the kink antikink wave respectively appearing in the stable region out of the coexisting curve near the spinodal line and in the unstable region within the spinodal line it is shown numerically that the triangular shock wave and the soliton wave are determined by the initial perturbation configuration and different initial perturbations will produce different waveforms in the stable region or near the spinodal line

traffic behavior in a mixture of different vehicles the car following models are extended to take into account the characteristics of different vehicles the characteristic of each car can be included in the parameter of the dimensionless delay time the traffic behavior is investigated analytically and numerically under the periodic boundary condition at a low density all the vehicles move at a constant velocity when the density is larger than the critical value the traffic flow becomes unstable and the density waves appear the jamming transition does not depend only on the mean value of the dimensionless delay time but also on the variation with increase in the variation of dimensionless delay time the jamming transition occurs at a higher value of the mean value it is found that the variation of vehicles stabilizes the traffic flow and suppresses the traffic jams the transition line obtained by the linear stability analysis is compared with the simulation result

mappings of finite distortion the degree of regularity this paper investigates the self improving integrability properties of the so called mappings of finite distortion let k x 1 be a measurable function defined on a domain rn n 2 and such that exp k x lloc1 0 we show that there exist two universal constants c1 n c2 n with the following property let f be a mapping in wloc1 1 rn with df x n k x j x f for a e x and such that the jacobian determinant j x f is locally in l1log c1 n l then automatically j x f is locally in l1logc2 n l this result constitutes the appropriate analog for the self improving regularity of quasiregular mappings and clarifies many other interesting properties of mappings of finite distortion namely we obtain novel results on the size of removable singularities for bounded mappings of finite distortion and on the area distortion under this class of mappings

gradient regularity for elliptic equations in the heisenberg group abstract we give dimension free regularity conditions for a class of possibly degenerate sub elliptic equations in the heisenberg group exhibiting super quadratic growth in the horizontal gradient this solves an issue raised in j j manfredi g mingione regularity results for quasilinear elliptic equations in the heisenberg group math ann 339 2007 485 544 where only dimension dependent bounds for the growth exponent are given we also obtain explicit a priori local regularity estimates and cover the case of the horizontal p laplacean operator extending some regularity proven in a domokos j j manfredi c 1 regularity for p harmonic functions in the heisenberg group for p near 2 in contemp math vol 370 2005 pp 17 23 in turn using some recent techniques of caffarelli and peral l caffarelli i peral on w 1 p estimates for elliptic equations in divergence form comm pure appl math 51 1998 1 21 the a priori estimates found are shown to imply the suitable local calderon zygmund theory for the related class of non homogeneous possibly degenerate equations involving discontinuous coefficients these last results extend to the sub elliptic setting a few classical non linear euclidean results t iwaniec projections onto gradient fields and l p estimates for degenerated elliptic operators studia math 75 1983 293 312 e dibenedetto j j manfredi on the higher integrability of the gradient of weak solutions of certain degenerate elliptic systems amer j math 115 1993 1107 1134 and to the non linear case estimates of the same nature that were available in the sub elliptic setting only for solutions to linear equations

smallness and cancellation in some elliptic systems with measure data abstract in a bounded open subset r n we study dirichlet problems with elliptic systems involving a finite radon measure on r n with values into r n defined by div a x u x d u x in u 0 on where a i x y 1 n j 1 n a i j x y j with 1 n the equation index we prove the existence of a distributional solution u r n obtained as the limit of approximations by assuming i that coefficients a i j are bounded caratheodory functions ii ellipticity of the diagonal coefficients a i j and iii smallness of the quadratic form associated to the off diagonal coefficients a i j i e verifying a r staircase support condition with r 0 such a smallness condition is satisfied for instance in each one of these cases a a i j a j i skew symmetry b a i j is small c a i j may be decomposed into two parts the first enjoying skew symmetry and the second being small in absolute value we give an example that satisfies our hypotheses but does not satisfy assumptions introduced in previous works a brezis s type nonexistence result is also given for general smooth elliptic hyperbolic systems

embedding bergman spaces into tent spaces let a p omega denote the bergman space in the unit disc mathbb d of the complex plane induced by a radial weight omega with the doubling property int r 1 omega s ds le c int frac 1 r 2 1 omega s ds the tent space t q s nu omega consists of functions such that begin aligned begin aligned vert f vert t q s nu omega q int mathbb d left int vargamma zeta f z s d nu z right frac q s omega zeta da zeta infty quad 0 q s infty end aligned end aligned here vargamma zeta is a non tangential approach region with vertex zeta in the punctured unit disc mathbb d setminus 0 we characterize the positive borel measures nu such that a p omega is embedded into the tent space t q s nu omega where 1 frac s p frac s q 0 by considering a generalized area operator the results are provided in terms of carleson measures for a p omega

quasilinear elliptic systems with measure data abstract we study the existence of solutions of quasilinear elliptic systems involving n equations and a measure on the right hand side with the form i 1 n x i 1 n j 1 n a i j x u x j u in u 0 on where 1 n is the equation index is an open bounded subset of r n u r n and is a finite randon measure on r n with values in r n existence of a solution is proved for two different sets of assumptions on a examples are provided that satisfy our conditions but do not satisfy conditions required on previous works on this matter

stability for p laplace type equation in a borderline case abstract we study the dirichlet problem for a p laplacian type operator in the setting of the orlicz zygmund space q log r n q 1 and 0 more precisely our aim is to establish under which assumptions on 0 existence and uniqueness of the solution are assured and to prove continuity and stability of the associated nonlinear operator

on non linear elliptic equation with weight abstract in this paper we prove the existence and uniqueness theorem of the dirichlet problem for certain non linear elliptic operators with muckenhoupt weight

higher integrability of very weak solutions of systems of p x laplacean type abstract we prove higher integrability of very weak solutions of a class of nonlinear elliptic systems whose model is the p x laplacean system div d u p x 2 d u div f p x 2 f i e we show that for small enough a function which solves the system and has bounded p x 1 energy satisfies d u p x l loc 1

numerical simulation of soliton and kink density waves in traffic flow with periodic boundaries abstract the soliton and kink antikink density waves are simulated with periodic boundaries by adding perturbation in the initial condition on single lane road based on a car following model they are reproduced in the form of the space time evolution of headway both of which propagate backwards it is found that the solitons appear only near the neutral stability line regardless of the boundary conditions and they exhibit upward form when the initial headway is smaller than the safety distance otherwise they exhibit downward form comparison is made between the numerical and analytical results about the amplitude of kink antikink wave and the underlying mechanism is analyzed besides it is indicated that the maximal current of traffic flow increases with decreasing safety distance the numerical simulation shows a good agreement with the analytical results

nonlinear potential theory of elliptic systems abstract we give a summary of recent results from nonlinear potential theory focusing on linear and nonlinear potential estimates of solutions to non homogeneous equations and systems we start with the cases of quasilinear possibly degenerate equations of p laplacian type and passing through fully nonlinear elliptic equations finally move to systems in this last case we describe recent results implying potential estimates for the p laplacian system finally we describe results bridging nonlinear potential theory and classical partial regularity theory for general elliptic systems the main outcomes are new e regularity criteria involving both excess functionals and nonlinear potentials

overview of differential equations with non standard growth abstract differential equations with non standard growth have been a very active field of investigation in recent years in this survey we present an overview of the field as well as several of the most important results we consider both existence and regularity questions finally we provide a comprehensive list of papers published to date

derivation and empirical validation of a refined traffic flow model abstract the gas kinetic foundation of fluid dynamic traffic equations suggested in previous papers d helbing physica a 219 1995 375 and 391 is further refined by applying the theory of dense gases and granular materials to the boltzmann like traffic model by paveri fontana it is shown that despite the phenomenologically similar behaviour or ordinary and granular fluids the relations for these cannot directly be transferred to vehicular traffic the dissipative and anisotropic interactions of vehicles as well as their velocity dependent space requirements lead to a considerably different structure of the macroscopic traffic equations also in comparison with the previously suggested traffic flow models as a consequence the instability mechanisms of emergent density waves are different crucial assumptions are validated by empirical traffic data and essential results are illustrated by figures

regularity of solutions of degenerate a harmonic equations we study the regularity of solutions to degenerate a harmonic equations under suitable integrability assumptions on the ellipticity and growth coefficients in particular we show a self improving property of the gradient of the solutions extending previous results by gehring and iwaniec sbordone valid in the uniformly elliptic setting

deterministic models for traffic jams abstract we study several deterministic one dimensional traffic models for integer positions and velocities we find the typical high and low density phases separated by a simple transition if positions and velocities are continuous variables the model shows self organized critically driven by the slowest car

a distance between orbits that controls commutator estimates and invertibility of operators abstract a distance between orbit spaces generated by a single element is introduced and it is shown that if an operator is invertible in one orbit it is also invertible in nearby orbits thus proving a version of shneiberg s theorem for orbital methods the same machinery is used to extend the celebrated rochberg weiss commutator theorem to the setting of orbital methods it is shown that these results apply to the real and complex methods of interpolation by proving that these methods can be suitably obtained as orbits of a single element

imbedding potentials in tent spaces abstract we obtain characterizations of positive borel measures on b n so that the nonisotropic potential space k lp d is imbedded in the tent space t2q d where 1 q we deduce characterizations for pointwise multipliers of the space h p

nonlinear commutators for the fractional p laplacian and applications we prove a nonlinear commutator estimate concerning the transfer of derivatives onto testfunctions for the fractional p laplacian this implies that solutions to certain degenerate nonlocal equations are higher differentiable also weakly fractional p harmonic functions which a priori are less regular than variational solutions are in fact classical as an application we show that sequences of uniformly bounded frac n s harmonic maps converge strongly outside at most finitely many points

a unified theory of commutator estimates for a class of interpolation methods abstract a general family of interpolation methods is introduced which includes as special cases the real and complex methods and also the so called or g1 and g2 methods defined by peetre and gustavsson peetre derivation operators and translation operators r are introduced for all methods of this family a theorem is proved about the boundedness of the commutators t and t r for operators t which are bounded on the spaces of the pair to which the interpolation method is applied this extends and unifies results previously known for derivation and translation operators in the contexts of the real and complex methods other results deal with higher order commutators and also include an equivalence theorem i e it is shown that as previously known only for real interpolation spaces all these interpolation spaces have two different equivalent definitions in the style of the j method and k method auxiliary results which may also be of independent interest include the equivalence of lions schechter complex interpolation spaces defined using an annulus with the same spaces defined in the usual way using a strip

convergence and decay rate to equilibrium of bounded solutions of quasilinear parabolic equations abstract we study the convergence and decay rate to equilibrium of bounded solutions of the quasilinear parabolic equation u t div a x u f x u 0 on a bounded domain subject to dirichlet boundary and to initial conditions the data are supposed to satisfy suitable regularity and growth conditions our approach to the convergence result and decay estimate is based on the ojasiewicz simon gradient inequality which in the case of the semilinear heat equation is known to give optimal decay estimates the abstract results and their applications are discussed also in the framework of orlicz sobolev spaces

nonlinear analysis of a differential difference equation with next nearest neighbour interaction for traffic flow we analyse the newell whitham type car following model described by a differential difference equation with a generalized optimal velocity function which depends not only on the headway of each car but also on the headway of the immediately preceding one linear stability analysis shows that the model is stabilized for larger delay time by taking into account the headway of the immediately preceding car from the nonlinear analysis the propagating kink solution for traffic jams is obtained the fundamental diagram and the relation between the headway and the delay time are examined by numerical simulation we find that the result from the nonlinear analysis is in good agreement with that obtained from the numerical simulation

on coercive variational integrals abstract it is well known that sequential weak lower semicontinuity of a variational integral f u f u x d x on the sobolev space w 1 p r n under a p growth condition on the integrand f is equivalent to quasiconvexity in the sense of morrey we show that coercivity on dirichlet classes likewise is equivalent to a quasiconvexity condition we also discuss some examples and extend a sequential weak lower semicontinuity result to the case of signed integrands

higher differentiability for n harmonic systems with sobolev coefficients abstract we provide a higher differentiability result for the finite energy solutions u w 1 1 r n of a degenerate elliptic system of the form div a x d u 0 in r n where is a bounded open set in r n and a x is a degenerate elliptic operator the function which measures the degree of degeneracy of the problem is assumed to belong to the sobolev class w 1 n

jamming transition in pedestrian counter flow a lattice gas model with biased random walkers is presented to mimic the pedestrian counter flow in a channel under the open boundary condition of constant density there are two types of walkers without the back step the one is the random walker going to the right and the other is the random walker going to the left it is found that a dynamical jamming transition from the freely moving state at low density to the stopped state at high density occurs at the critical density the transition point is given by pc 0 45 0 01 not depending on the system size the transition point depends on the strength of drift and decreases with increasing drift also we present the extended model to take into account the traffic rule in which a pedestrian walks preferably on the right hand side of the channel

regularity in oscillatory nonlinear elliptic systems we give uniform bounds in morrey sobolev spaces h1 for weak solutions ue to oscillatory nonlinear elliptic systems the main novelty is in the precise qualitative description of the e uniform morrey exponent in terms of the ellipticity ratio of the elliptic systems this is achieved by showing that weak solutions of general nonlinear elliptic systems with lipschitz coefficients are of class w2 p locally or globally depending on assumptions for an exponent p 2 that is independent of dimensions and for which p 2 is inversely proportional to the ellipticity ratio

phase diagram of a non signalized t shaped intersection abstract in this paper we investigated a non signalized t shaped intersection using the cellular automata model under the open boundary condition two different priority rules at intersection are introduced rule 1 rule 2 to eliminate the jam packed state phase diagram and its variation with the ratios of right and or left turning vehicles are investigated the space time and the density profiles are also studied the simulation results indicate that the system does not show the same performance under different priority rules where rule 1 resp rule 2 can be better than rule 2 resp rule 1 according to the ratios of turning vehicles

hyperelastic deformations of smallest total energy throughout this article mathbb x and mathbb y will be nonempty bounded domains in mathbb r n n geqq 2 the term deformation of mathbb x subset mathbb r n onto mathbb y subset mathbb r n refers to an orientation preserving homeomorphism h mathbb x overset textnormal tiny onto longrightarrow mathbb y in the sobolev class fancyscript w 1 1 mathbb x mathbb y whose inverse f mathbb y overset textnormal tiny onto longrightarrow mathbb x lies in fancyscript w 1 1 mathbb y mathbb x the general law of hyperelasticity asserts that there exists an energy integral mathcal e mathbb x h int mathbb x e x h dh rm dx such that the elastic deformations have the smallest energy we assume here that e is conformally coerced and polyconvex some additional regularity conditions are also imposed under those conditions we establish the existence and global invertibility of the minimizers the key tools in obtaining an extremal deformation h mathbb x overset textnormal tiny onto longrightarrow mathbb y regardless of its boundary values are the free lagrangians finding suitable free lagrangians and using them for a specific stored energy function e is truly a work of art we have done it here for the so called total harmonic energy and a pair of annuli in the plane in fact this challenging problem illustrates rather clearly the strength of the concept of free lagrangians