lp gradient estimate for elliptic equations with high contrast conductivities in rn abstract uniform estimate for the solutions of elliptic equations with high contrast conductivities in r n is concerned the space domain consists of a periodic connected sub region and a periodic disconnected matrix block subset the elliptic equations have fast diffusion in the connected sub region and slow diffusion in the disconnected subset suppose 0 1 is the diameter of each matrix block and 2 0 1 is the conductivity ratio of the disconnected matrix block subset to the connected sub region it is proved that the w 1 p norm of the elliptic solutions in the connected sub region is bounded uniformly in when the l p norm of the elliptic solutions in the whole space is bounded uniformly in the w 1 p norm of the elliptic solutions in perforated domains is bounded uniformly in however the l p norm of the second order derivatives of the solutions in the connected sub region may not be bounded uniformly in

hessian estimates in orlicz spaces for fourth order parabolic systems in non smooth domains abstract we establish the global hessian estimate in orlicz spaces for a fourth order parabolic system with discontinuous tensor coefficients in a non smooth domain under the assumptions that the coefficients have small weak bmo semi norms the boundary of a domain is reifenberg flat for 0 small and the given young function satisfies some moderate growth condition as a corollary we obtain an optimal global w 2 p regularity for such a system

parabolic equations with measurable coefficients ii we prove the existence and uniqueness of solutions in sobolev spaces to second order parabolic equations in non divergence form the coefficients except one of them of second order terms of the equations are measurable in both time and one spatial variables and vmo vanishing mean oscillation in other spatial variables

weighted gradient estimates for elliptic problems with neumann boundary conditions in lipschitz and semi convex domains abstract let n 2 and be a bounded lipschitz domain in r n in this article the authors investigate global weighted norm estimates for the gradient of solutions to neumann boundary value problems of second order elliptic equations of divergence form with real valued bounded measurable coefficients in more precisely for any given p 2 two necessary and sufficient conditions for w 1 p estimates of solutions to neumann boundary value problems respectively in terms of a weak reverse holder inequality with exponent p or weighted w 1 q estimates of solutions with q 2 p and some muckenhoupt weights are obtained as applications for any given p 1 and a p r n the class of muckenhoupt weights the authors establish weighted w 1 p estimates for solutions to neumann boundary value problems of second order elliptic equations of divergence form with small bmo coefficients on bounded semi convex domains as further applications the global gradient estimates are obtained respectively in weighted lorentz spaces lorentz morrey spaces weighted orlicz spaces and variable lebesgue spaces

quasilinear elliptic equations with bmo coefficients in lipschitz domains we obtain a global estimate for the weak solution to an elliptic partial differential equation of laplacian type with bmo coefficients in a lipschitz domain with small lipschitz constant

uniformly nondegenerate elliptic equations with partially bmo coefficients in nonsmooth domains abstract a global estimate in weighted lorentz sobolev spaces is obtained for the weak solutions to divergence form uniformly nondegenerate elliptic equations over a bounded nonsmooth domain here the leading coefficients are assumed to be merely measurable in one variable and have small bmo semi norms in the remaining variables under the assumption that one variable direction is perpendicular to the boundary points which is close to the boundary while a geometric assumption on the boundary is a locally bounded reifenberg flatness in addition we also investigate regularities in lorentz morrey morrey and holder spaces for elliptic equations under the same assumptions on the leading coefficients and the boundary of domain

weighted regularity estimates for a class of higher order nonlinear parabolic and elliptic systems abstract in this paper we prove the weighted l p regularity estimates and the morrey regularity estimates for a class of higher order nonlinear parabolic systems which satisfy an asymptotically regular condition as a byproduct similar regularity estimates are also obtained for a corresponding class of higher order nonlinear elliptic systems

a linear time algorithm for obtaining the convex hull of a simple polygon in this paper a linear time algorithm is described for finding the convex hull of a simple i e non self intersecting polygon

non uniform elliptic equations in convex lipschitz domains abstract non uniform elliptic equations in convex lipschitz domains are concerned the non smooth domains consist of a periodic connected high permeability sub region and a periodic disconnected matrix block subset with low permeability let 0 1 denote the size ratio of the matrix blocks to the whole domain and let 2 0 1 denote the permeability ratio of the disconnected matrix block subset to the connected sub region the w 1 p norm for p 1 of the elliptic solutions in the high permeability sub region is shown to be bounded uniformly in however the w 1 p norm of the solutions in the low permeability subset may not be bounded uniformly in roughly speaking if the sources in the low permeability subset are small enough the solutions in that subset are bounded uniformly in otherwise the solutions cannot be bounded uniformly in relations between the sources and the variation of the solutions in the low permeability subset are also presented in this work

on the unequal error protection for progressive image transmission in this paper we consider the unequal error protection uep for progressive image transmission when the coded packet size is fixed first we prove that for the source code with convex rate distortion r d function and practically used channel codes the channel code rate for each packet in the optimal rate allocation is nondecreasing indeed then we give an upper bound for the channel code rate of the last packet so that the number of rate allocations in the exhaustive search can be predicted further we propose a heuristic optimization method which has low complexity and obtains performance approaching to the optimal solutions for various channel conditions and transmission rates

global regularity for divergence form elliptic equations on quasiconvex domains abstract in this paper we introduce a notion of quasiconvex domain and show that the global w 1 p regularity holds on such domains for a wide class of divergence form elliptic equations the modified vitali covering lemma compactness method and the maximal function technique are the main analytical tools

local holder regularity for solutions of elliptic systems in this note we prove local l p regularity for the highest order derivatives of an elliptic system of arbitrary order in nondivergence form where the coefficients of the principal part are taken in the space of sarason vanishing mean oscillation vmo lower order coefficients and the known term belong to suitable lebesgue spaces as

w1 p estimates for elliptic problems with neumann boundary conditions in lipschitz domains abstract we study w 1 p estimates in lipschitz domains for second order elliptic equations and systems of divergence form with real valued bounded measurable coefficients for any fixed p 2 we prove that a weak reverse holder inequality implies the w 1 p estimates for solutions with neumann boundary conditions as a result we are able to show that if the coefficient matrix of elliptic equation is symmetric and in vmo r n the w 1 p estimate holds for 3 2 e p 3 e if n 3 and for 4 3 e p 4 e if n 2 and for elliptic systems the w 1 p estimate is true for 2 n n 1 e p 2 n n 1 e

higher order nondivergence elliptic and parabolic equations in sobolev spaces and orlicz spaces abstract in this paper we obtain the global regularity estimates of the solutions in sobolev spaces and orlicz spaces for higher order elliptic and parabolic equations of nondivergence form in the whole space we only need to focus on the parabolic case since the corresponding result in the elliptic case can be obtained as a corollary

finding the convex hull of a simple polygon in linear time abstract though linear algorithms for finding the convex hull of a simply connected polygon have been reported not all are short and correct a compact version based on sklansky s original idea 7 and bykat s counter example 8 is given its complexity and correctness are also shown

parabolic equations with vmo coefficients in sobolev spaces with mixed norms an lq lp theory of divergence and non divergence form parabolic equations is presented the main coefficients are supposed to belong to the class vmox which in particular contains all measurable functions depending only on t the method of proving simplifies the methods previously used in the case p q

elliptic equations with bmo coefficients in reifenberg domains the inhomogeneous dirichlet problems concerning divergence form elliptic equations are studied optimal regularity requirements on the coefficients and domains for the w1 p theory 1 p are obtained the principal coefficients are supposed to be in the john nirenberg space with small bmo seminorms the domain is a reifenberg domain these conditions for the w1 p theory not only weaken the requirements on the coefficients but also lead to a more general geometric condition on the domains in fact these domains might have fractal dimensions 2004 wiley periodicals inc

on a convex hull algorithm for polygons and its application to triangulation problems abstract a frequently used algorithm for finding the convex hull of a simple polygon in linear running time has been recently shown to fail in some cases due to its simplicity the algorithm is nevertheless attractive in this paper it is shown that the algorithm does in fact work for a family of simple polygons known as weakly externally visible polygons some application areas where such polygons occur are briefly discussed in addition it is shown that with a trivial modification the algorithm can be used to internally and externally triangulate certain classes of polygons in 0 n time

global morrey regularity of strong solutions to the dirichlet problem for elliptic equations with discontinuous coefficients abstract well posedness is proved in the space w2 p w1 p0 for the dirichlet problem equation omitted if the principal coefficients aij x of the uniformly elliptic operator belong to vmo l

global regularity for divergence form elliptic equations in orlicz spaces on quasiconvex domains abstract in this paper we derive the global regularity of weak solutions to divergence form elliptic equations in the orlicz space w 0 1 l with 2 2 the domain considered here is quasiconvex which is a generalization of the reifenberg flat domain

a new proof of lp estimates of stokes equations abstract in this paper we establish a new proof of l p estimates of the stokes equations which enables us to avoid the use of potential theory and thus simplifies the traditional proof the modified vitali covering lemma and the maximal function technique are the main analytical tools

global holder continuity of weak solutions to quasilinear divergence form elliptic equations abstract we derive global holder regularity for the w 0 1 2 weak solutions to the quasilinear uniformly elliptic equation div a i j x u d j u a i x u a x u d u 0 over a c 1 smooth domain r n n 2 the nonlinear terms are all of caratheodory type with coefficients a i j x u belonging to the class vmo of functions with vanishing mean oscillation with respect to x while a i x u and a x u d u exhibit controlled growths with respect to u and the gradient du

on maximal parabolic regularity for non autonomous parabolic operators abstract we consider linear inhomogeneous non autonomous parabolic problems associated to sesquilinear forms with discontinuous dependence of time we show that for these problems the property of maximal parabolic regularity can be extrapolated to time integrability exponents r 2 this allows us to prove maximal parabolic l r regularity for discontinuous non autonomous second order divergence form operators in very general geometric settings and to prove existence results for related quasilinear equations

a weighted lp theory for divergence type parabolic pdes with bmo coefficients on c1 domains abstract in this paper we present a weighted l p theory of parabolic equations of divergence type defined on c 1 domains the leading coefficients have vmo vanishing mean oscillation or small bmo bounded mean oscillation and lower order coefficients are allowed to be unbounded and to blow up near the boundary

uniform w 1 p estimates for systems of linear elasticity in a periodic medium abstract let l e be a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients we obtain the uniform w 1 p estimate u e p c f p in a lipschitz domain in r n for solutions to the dirichlet problem l e u e div f in and u e 0 on where 1 p 1 2 1 2 n and c 0 are constants independent of e 0 the ranges are sharp for n 2 or 3

higher integrability for nonlinear elliptic equations with variable growth and discontinuous coefficients abstract in this paper based on the theory of variable exponent spaces we study the higher integrability for a class of nonlinear elliptic equations with variable growth and discontinuous coefficients under suitable assumptions we obtain a local gradient estimate in orlicz space for weak solution

gradient estimates for a class of parabolic systems we establish local calderon zygmund type estimates for a class of parabolic problems whose model is the nonhomogeneous degenerate singular parabolic p laplacian system ut div du p 2du div f p 2f proving that f lqloc du lqloc q p we also treat systems with discontinuous coefficients of vanishing mean oscillation vmo type

calderon zygmund estimates for stochastic homogenization abstract we prove quenched l p type estimates for the gradient of a solution of a quasilinear elliptic equation with random coefficients

solvability of parabolic equations in divergence form with partially bmo coefficients abstract we prove the h p 1 solvability of second order parabolic equations in divergence form with leading coefficients a i j measurable in t x 1 and having small bmo bounded mean oscillation semi norms in the other variables additionally we assume a 11 is measurable in x 1 and has small bmo semi norms in the other variables the corresponding results for the cauchy problem are also established parabolic equations in sobolev spaces h q p 1 with mixed norms are also considered under the same conditions of the coefficients

solvability for schrodinger equations with discontinuous coefficients abstract we consider the l p solvability for divergence and non divergence form schrodinger equations with discontinuous coefficients as an application we give the global morrey regularity for divergence and non divergence form schrodinger operators with vmo coefficients in a bounded domain

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

the conormal derivative problem for elliptic equations with bmo coefficients on reifenberg flat domains we study the inhomogeneous conormal derivative problem for the divergence form elliptic equation assuming that the principal coefficients belong to the bmo space with small bmo semi norms and that the boundary is delta reifenberg flat these conditions for the w 1 p theory not only weaken the requirements on the coefficients but also lead to a more general geometric condition on the domain in fact the reifenberg flatness is the minimal regularity condition for the w 1 p theory

hs p regularity theory for a class of nonlocal elliptic equations abstract in this paper we study the regularity of weak solutions to a class of nonlocal elliptic equations in bessel potential spaces h s p our main results can be seen as an extension of the well known w 1 p regularity theory for local second order elliptic equations in divergence form to the nonlocal setting

second order elliptic equations with variably partially vmo coefficients abstract the solvability in w p 2 r d spaces is proved for second order elliptic equations with coefficients which are measurable in one direction and vmo in the orthogonal directions in each small ball with the direction depending on the ball this generalizes to a very large extent the case of equations with continuous or vmo coefficients

gradient estimates for elliptic systems in non smooth domains we obtain the global w 1 p 1 p estimate for the weak solution of an elliptic system with discontinuous coefficients in non smooth domains without using maximal function approach it is assumed that the boundary of a bounded domain is well approximated by hyperplanes at every point and at every scale and that the tensor coefficients belong to bmo space with their bmo semi norms sufficiently small

higher order elliptic operators of divergence form in c1 or lipschitz domains abstract we consider a 2 m th order elliptic operator of divergence form in a domain of r n whose leading coefficients are uniformly continuous in the paper y miyazaki the l p theory of divergence form elliptic operators under the dirichlet condition j differential equations 215 2005 320 356 we developed the l p theory including the construction of l p resolvents assuming that the boundary of is of class c m 1 the purpose of this paper is to show that the l p theory also holds when is a c 1 domain applying the inequalities of hardy type for the sobolev spaces

generalized morrey estimates for the gradient of divergence form parabolic operators with discontinuous coefficients abstract we consider the cauchy dirichlet problem for linear divergence form parabolic operators in bounded reifenberg flat domains the coefficients are supposed to be only measurable in one of the space variables and small bmo with respect to the others we obtain boundedness of the hardy littlewood maximal operator in the generalized morrey spaces w p p 1 and weight satisfying certain supremum condition this permits us to obtain calderon zygmund type estimate for the gradient of the weak solution of the problem

applications of the differential calculus to nonlinear elliptic operators with discontinuous coefficients the paper concerns dirichlet s problem for second order quasilinear non divergence form elliptic equations with discontinuous coefficients we start with suitable structure growth and regularity conditions ensuring solvability of the problem under consideration fixing then a solution u 0 such that the linearized at u 0 problem is non degenerate we apply the implicit function theorem as a result we get that for all small perturbations of the coefficients there exists exactly one solution u u 0 which depends smoothly in w 2 p with p larger than the space dimension on the data for that no structure and growth conditions are needed and the perturbations of the coefficients can be general l functions of the space variable x moreover we show that the newton iteration procedure can be applied in order to obtain a sequence of approximate in w 2 p solutions for u 0

free boundary regularity for harmonic measures and poisson kernels one of the basic aims of this paper is to study the relationship between the geometry of hypersurface like subsets of euclidean space and the properties of the measures they support in this context we show that certain doubling properties of a measure determine the geometry of its support a radon measure is said to be doubling with constant c if c times the measure of the ball of radius r centered on the support is greater than the measure of the ball of radius 2r and the same center we prove that if the doubling constant of a measure on r n 1 is close to the doubling constant of the ndimensional lebesgue measure then its support is well approximated by ndimensional a ne spaces provided that the support is relatively at to start with primarily we consider sets which are boundaries of domains in r n 1 the n dimensional hausdorfi measure may not be deflned on the boundary of a domain in r n 1 thus we turn our attention to the harmonic measure which is well behaved under minor assumptions see section 3 we obtain a new characterization of locally at domains in terms of the doubling properties of their harmonic measure see section 3 along these lines we investigate how the weak regularity of the poisson kernel of a domain determines the geometry of its boundary sections 5 and 6 pursue this goal as in alt and cafiarelli s work see ac c1 c2 and also jerison s j in both cases the goal is to prove that under the appropriate technical conditions at at points of the boundary the oscillation of the poisson kernel controls the oscillation of the unit normal vector the difierence between our work and the work in ac is that we measure the oscillation in an integral sense bmo estimates

global regularity for higher order divergence elliptic and parabolic equations abstract in this paper we obtain the global regularity estimates of the weak solutions in sobolev spaces and orlicz spaces for higher order elliptic and parabolic equations of divergence form with small bmo coefficients in the whole space we only focus on the parabolic case while the corresponding result in the elliptic case can be obtained as a corollary

on w1 p estimates for elliptic equations in divergence form first we will apply the method to study w 1 p regularity for a nonlinear elliptic operator in divergence form we would like to point out that in the particular case of a linear elliptic equation this method gives an alternative proof to the classical one which uses the general theory of singular integrals the utility of the method that we describe below is that hypotheses a and b are obtained directly by studying the deviation of the coefficients of a from the coefficients of a0 and this is usually not a difficult task a more interesting application of this kind of approximation method is to elliptic homogenization problems for which we obtain results that give w 1 p estimates with a weak hypothesis of regularity in the coefficients for instance we are able to study the following cases

l p estimates for parabolic equations in reifenberg domains abstract the inhomogeneous neumann problem for parabolic equations in divergence form is studied an optimal regularity requirement on the domain for the l p theory is investigated assuming that the principal coefficients are supposed to be in the john nirenberg space with small bmo semi norms and that the domain is a reifenberg flat domain

elliptic equations in divergence form with partially bmo coefficients the solvability in sobolev spaces is proved for divergence form second order elliptic equations in the whole space a half space and a bounded lipschitz domain for equations in the whole space or a half space the leading coefficients aij are assumed to be only measurable in one direction and have locally small bmo semi norms in the other directions for equations in a bounded domain additionally we assume that aij have small bmo semi norms in a neighborhood of the boundary of the domain we give a unified approach of both the dirichlet boundary problem and the conormal derivative problem we also investigate elliptic equations in sobolev spaces with mixed norms under the same assumptions on the coefficients

lp regularity for fourth order parabolic systems with measurable coefficients we treat fourth order parabolic systems in divergence form with bounded measurable coefficients we establish hessian estimates for such parabolic systems by proving that the lp regularity of the inhomogeneous terms exactly reflects in the regularity of the hessian of the solutions for every p in 1 infty the assumptions are that the coefficients are allowed to be merely measurable in one of spatial variables but averaged in the other spatial variables and time variable

square roots of elliptic second order divergence operators on strongly lipschitz domains l p theory we study l p estimates for square roots of second order elliptic non necessarily selfadjoint operators in divergence form l mathrm div a nabla on lipschitz domains subject to dirichlet or to neumann boundary conditions pursuing our work 4 where we considered operators on mathbb r n we obtain among other things l 1 2 f p le c nabla f p for all 1 p infty if l is real symmetric and the domain bounded which is new for 1 p 2 we also obtain similar results for perturbations of constant coefficients operators our methods rely on a singular integral representation calderon zygmund theory and quadratic estimates a feature of this study is the use of a commutator between the resolvent of the laplacian dirichlet and neumann and partial derivatives which carries the geometry of the boundary

linear second order divergence equations in lipschitz domains abstract in this paper we generalize gradient estimates in l p spaces to orlicz spaces for weak solutions of second order divergence elliptic equations with small bmo coefficients in lipschitz domains our results improve the known results for such equations using the harmonic analysis method

a weighted l p theory for parabolic pdes with bmo coefficients on c 1 domains abstract in this paper we present a weighted l p theory of second order parabolic partial differential equations defined on c 1 domains the leading coefficients are assumed to be measurable in time variable and have vmo vanishing mean oscillation or small bmo bounded mean oscillation with respect to space variables and lower order coefficients are allowed to be unbounded and to blow up near the boundary our bmo condition is slightly relaxed than the others in the literature

elliptic equations with bmo coefficients in lipschitz domains in this paper we study inhomogeneous dirichlet problems for elliptic equations in divergence form optimal regularity requirements on the coefficients and domains for the w 1 p 1 p estimates are obtained the principal coefficients are supposed to be in the john nirenberg space with small bmo semi norms the domain is supposed to have lipschitz boundary with small lipschitz constant these conditions for the w 1 p theory do not just weaken the requirements on the coefficients they also lead to a more general geometric condition on the domain

quasilinear parabolic operators with discontinuous ingredients let q 0 t r n 1 be a cylinder of height t 0 and c1 1 smooth base unique strong solvability in the sobolev spaces wq2 1 q q n 2 is proved for oblique derivative boundary value problem for quasilinear nondivergence form strictly parabolic equation with vanishing mean oscillation coefficients ut aij x t u diju f x t u du a e in q where aij and f are caratheodory s functions an essential step of our investigations is deriving of suitable a priori estimates for the solution and its spatial gradient which makes possible the application of leray schauder s fixed point theorem

parabolic equations with bmo coefficients in lipschitz domains abstract in this paper we are concerned with certain natural sobolev type estimates for weak solutions of inhomogeneous problems for second order parabolic equations in divergence form the geometric setting is that of time independent cylinders having a space intersection assumed to be locally given by graphs with small lipschitz coefficients the constants of the operator being uniformly parabolic we prove the relevant l p estimates assuming that the coefficients are in parabolic bounded mean oscillation bmo and that their parabolic bmo semi norms are small enough

error protection for progressive image transmission over memoryless and fading channels product channel codes are proposed to protect progressively compressed and packetized images for noisy channels within packets the product code uses the concatenation of a rate compatible punctured convolutional code and an error detecting parity check code across packets reed solomon codes are used benefits include flexible choice of delay adaptability of error protection level i e unequal error protection and scalable decoding complexity the system outperforms the best known image coders for memoryless channels and performs well on fading channels

a linear time algorithm for computing the convex hull of an ordered crossing polygon in this paper we describe a linear time algorithm for finding the convex hull of an ordered crossing polygon and prove its correctness

the uniform hopf inequality for discontinuous coefficients and optimal regularity in bmo for singular problems abstract we consider some singular second order semilinear problems which include among many other special cases the boundary layer equations such as they were treated by o a oleinik in her pioneering works we consider diffusion linear operator with possible discontinuous coefficients and prove an optimal criterion to get a quantitative strong maximum principle that we call uniform hopf inequality uhi since the solutions of the singular semilinear problems under consideration are not lipschitz continuous we carry out a careful study of the regularity of solutions when the coefficients of the diffusion matrix are merely in the vmo space and bounded we prove that the gradient of the solution is still p integrable in absence of any continuity assumption on the spatial potential coefficient in the singular term to this end the uhi property is used several times we also apply and improve previous a priori estimates due to s campanato in 1965

hessian estimates for fourth order elliptic systems with singular bmo coefficients in composite reifenberg domains abstract we consider fourth order elliptic systems in divergence form with greatly discontinuous coefficients in a nonsmooth domain our domain is composed of a finite number of disjoint subdomains with r reifenberg flat boundaries and the coefficients which are allowed to have great discontinuity across the boundaries of subdomains have small bmo semi norms on each subdomain our main result is deriving the global w 2 p 1 p regularity with the estimates independent of the distance between the subdomains

fourth order parabolic equations with weak bmo coefficients in reifenberg domains abstract we study optimal w 2 p regularity for fourth order parabolic equations with discontinuous coefficients in general domains we obtain the global w 2 p regularity for each 1 p under the assumption that the coefficients have suitably small bmo semi norm of weak type and the boundary of the domain is reifenberg flat the situation of our main theorem arises when the conductivity on fractals is controlled by a random variable in the time direction

2 solvability of the dirichlet problem for nondivergence elliptic equations with vmo coefficients we prove a well posedness result in the class w 2 p w 0 1 p for the dirichlet problem lu f a e in u 0 on we assume the coefficients of the elliptic nondivergence form equation that we study are in vmo l

computing the convex hull of a simple polygon abstract an algorithm for computing the convex hull of a simple polygon is presented its correctness and complexity are also shown

w 1 p regularity for elliptic equations with measurable coefficients in nonsmooth domains we establish global w 1 p estimates for second order elliptic equations in divergence form under the natural assumption that p is log holder continuous to this end we assume that the coefficients are measurable in one variable and have small bmo semi norms in the other variables and the boundary of the domain is reifenberg flat our work is an optimal and natural extension of w 1 p regularity for such equations with merely measurable coefficients beyond lipschitz domains

parabolic equations in reifenberg domains natural sobolev type estimates are proved for weak solutions of inhomogeneous parabolic equations in divergence form in a bounded cylinder 0 t which is reifenberg flat in the space direction the principal coefficients of the operator are assumed to be in bmo space with their bmo semi norms small enough

interior w 1 p x t regularity for parabolic divergence equations of hormander s type abstract let x 1 x 2 x q be a system of real smooth vector fields satisfying hormander s condition in a bounded domain r n we consider the following parabolic equations u t x i a i j x t x j u x i f i in t where x i is the formal adjoint of x i the coefficients a i j x t are real valued measurable functions defined in t 0 t satisfying the uniform parabolic condition 0 1 2 i j 1 q a i j x t i j 1 2 for almost every x t r n r every r q and some constant we prove the interior w 1 p x t regularity for weak solutions to the parabolic equations under the assumptions that p x t satisfies the strong log holder continuity condition and the coefficients a i j x t belong to the space v m o l o c l our method relies on a gagliardo nirenberg inequality constituted on hormander s vector fields and a certain vitali covering lemma

unveiling turbo codes some results on parallel concatenated coding schemes a parallel concatenated coding scheme consists of two simple constituent systematic encoders linked by an interleaver the input bits to the first encoder are scrambled by the interleaver before entering the second encoder the codeword of the parallel concatenated code consists of the input bits to the first encoder followed by the parity check bits of both encoders this construction can be generalized to any number of constituent codes parallel concatenated schemes employing two convolutional codes as constituent codes in connection with an iterative decoding algorithm of complexity comparable to that of the constituent codes have been previously shown to yield remarkable coding gains close to theoretical limits they have been named and are known as turbo codes we propose a method to evaluate an upper bound to the bit error probability of a parallel concatenated coding scheme averaged over all interleavers of a given length the analytical bounding technique is then used to shed some light on some crucial questions which have been floating around in the communications community since the proposal of turbo codes

approximate polytope ensemble for one class classification in this work a new one class classification ensemble strategy called approximate polytope ensemble is presented the main contribution of the paper is threefold first the geometrical concept of convex hull is used to define the boundary of the target class defining the problem expansions and contractions of this geometrical structure are introduced in order to avoid over fitting second the decision whether a point belongs to the convex hull model in high dimensional spaces is approximated by means of random projections and an ensemble decision process finally a tiling strategy is proposed in order to model non convex structures experimental results show that the proposed strategy is significantly better than state of the art one class classification methods on over 200 datasets highlightsthe methodology uses a convex hull for modeling one class classification problems random projections are used to approximate the convex hull in high dimensional spaces expansions of the approximate hulls are considered to set the optimal operating point exhaustive validation is performed on three different typologies of problems