subelliptic p harmonic maps into spheres and the ghost of hardy spaces the story begins with the paper of muller 59 who for the sake of an application to nonlinear elasticity proved that if the jacobian determinant ju of a sobolev map u w 1 n loc rn rn is nonnegative then it belongs locally to l log l the result is quite intriguing since a priori holder inequality implies only that ju l1 and one does not suspect any higher integrability if one does not assume that ju is nonnegative then as coifman lions meyer and semmes 14 have proved ju belongs to the local hardy space h 1 loc since a nonnegative function belongs to the local hardy space if and only if it belongs locally to l log l the result of coifman lions meyer and semmes generalizes that of muller in fact coifman lions meyer and semmes proved more namely for 1 p the scalar product of a divergence free vector field e lp rn rn and a curl free vector field b lp p 1 rn rn belongs to the hardy space h 1 a priori holder inequality implies integrability of this expression only note that the jacobian is of this form the discovery that many algebraic expressions involving partial derivatives belong to the hardy space turned out to be important and widely applicable in nonlinear partial differential equations this was first shown by helein 40 41 42 let us describe briefly his result consider maps u bn s m from the n dimensional ball to the mdimensional sphere such that the p energy of u given by the functional

the time line interpolation method for large time step godunov type schemes abstract this paper describes the use of the time line interpolation procedure for the design of large time step godunov type schemes for systems of hyperbolic conservation laws in one dimension these schemes are based on a specific procedure to characterize the left and right states of the riemann problems at the cell interfaces when the courant number associated with the waves exceeds unity to do so the time line interpolation technique is used constant and linear reconstruction techniques are presented sonic or critical points are seen to be a source of difficulty in the algorithm and an appropriate treatment is proposed the algorithms are applied to the linear advection equation to the inviscid burgers equation and to the set of hyperbolic conservation laws that describe shallow water flow in one dimension these simulations show the superiority of the linear time reconstruction over the use of a constant time reconstruction when the linear reconstruction technique is used the modulus of the amplification factor of the scheme is equal to unity for all wave numbers inducing oscillations in the computed profile owing to the phase error the introduction of a slope limiter allows these oscillations to be eliminated but yields numerical diffusion thus restricting the range of applications of the scheme

correlation of power variables frequency domain abstract this publication is a third paper in a series considering the concept of power correlation power correlation is treated herein from a frequency domain viewpoint with major emphasis being placed on the power frequency response function pfrf a pfrf relates power at a driving point to power at another point in a vibratory system a theoretical formula for power frequency response function is derived and experimentally determined pfrf s are presented a pfrf is complex valued the real part relating the transfer of real power from one point in a system to another this function provides further insight into power flow in a vibratory system

correlation of power variables abstract cross correlation functions between input power fluctuations and system power fluctuations are derived for a gaussian process and sine wave process these cross correlation functions are referred to as power correlations and they contain both a constant term plus a fluctuating quantity the derivations show that for a linear system with no uncorrelated noise normalized correlations of squared fluctuations between the input and output should be equal to one experimental data obtained from tests on an electrical circuit validated analytically derived power correlation formulas power correlation functions can be used for determination of propagation times for power transmission and for other applications such as resonance testing

the obstacle problem for parabolic non divergence form operators of hormander type in this paper we establish the existence and uniqueness of strong solutions to the obstacle problem for a class of parabolic sub elliptic operators in non divergence form structured on a set of smo

inegalites de sobolev produit sur les groupes de lie nilpotents on generalise dans le cadre des groupes de lie nilpotents reels et connexes l inegalite classique due a gagliardo et nirenberg

weighted strongly elliptic operators on lie groups let h g u be a continuous representation of a lie group g by bounded operators g u g on the banach space x and let x g du denote the representation of the lie algebra g obtained by differentiation if a1 ad is a lie algebra basis of g ai du ai and a ai1 aik whenever i1 ik we consider the operators formula where the c are complex coefficients satisfying a weighted strongly elliptic condition in which different directions may have different weights this condition is such that the class of operators considered encompasses all the standard strongly elliptic operators we prove that the closure h of each such operator h generates a holomorphic semigroup s with holomorphy sector which contains a non empty subsector determined by the coefficients and independent of the representation moreover the semigroup s has a smooth representation independent kernel and we derive bounds on the kernel and all its derivatives finally we establish elliptic regularity properties for the operators and their powers and characterize the analytic and gevrey vectors as a corollary we derive optimal growth bounds for the eigenfunctions of the anharmonic oscillators p2m q2n

a time frequency formulation of optimum detection a time frequency formulation is proposed for the optimum detection of gaussian signals in white gaussian noise by choosing the wigner ville distribution as the basic time frequency tool it is shown that the corresponding receivers generally take the form of a correlation between time frequency structures matching mathematical optimality with a physically meaningful interpretation the case of low snr is examined and various examples are considered deterministic signal rayleigh fading signal random jitter and random time varying channel a general class of time frequency receivers is proposed which admits as limiting cases different known structures and its suboptimum performance is evaluated possible extensions to more elaborate situations including parameter estimation are mentioned

gaussian upper bounds for the heat kernels of some second order operators on riemannian manifolds abstract we describe a method of obtaining gaussian upper bounds on heat kernels which unifies and improves recent results for hypoelliptic operators in divergence form and for laplace beltrami operators on complete riemannian manifolds

lower bounds for densities of uniformly elliptic random variables on wiener space in this article we generalize the lower bound estimates for uniformly elliptic diffusion processes obtained by kusuoka and stroock we define the concept of uniform elliptic random variable on wiener space and show that with this definition one can prove a lower bound estimate of gaussian type for its density we apply our results to the case of the stochastic heat equation under the hypothesis of unifom ellipticity of the diffusion coefficient

wiener criterion for a class of degenerate elliptic operators abstract in this paper we give some geometric criteria analogous to wiener s poincare s and zaremba s criteria for the laplacian for the regularity of boundary points for the dirichlet problem relative to a class of partial differtial operators of the form j 1n xj2 fulfilling hormander s condition

frequency response functions for power power transfer ratio and coherence abstract the concept of frequency response functions for power variables was proposed in reference 3 where a convolution integral formula in the frequency domain was used to relate fluctuating power variables and to give the frequency response function for power this convolution integral is simplified in the present paper for several cases of varying bandwidth random force inputs and cosine wave force input to an oscillator which results in frequency response functions for power which are dependent on the type of force input coherence functions for power variables are also determined from theory theoretically derived results compare well to those obtained from experiments and these results are used to demonstrate the bandwidth sensitivity of coherence between power and velocity squared the zero frequency or d c value of the frequency response function for power is shown to be related to the system damping and system damping can be determined from an examination of this term several formulas are given for the calculation of system damping for different types of force input and degrees of freedom of a system also power transfer is associated with the zero frequency term of the frequency response function for power and other frequencies are associated with power fluctuations given the mobility functions of a system the power transfer and effective damping can be determined for any force bandwidth by the formulas given in this paper

correlation of power variables normalized results abstract correlation of fluctuating power input to a system and a fluctuating system field variable squared was examined in reference 1 in this paper the power correlation function is normalized for gaussian field variables and is shown to be the product of two normalized field correlation function and a weighting factor which is dependent upon statistics of force velocity and power at a driving point experiments on a rlc circuit validated results of derivations given in this paper and that given in reference 1 several relationships are derived in this paper associated with the force excitation of a structure and power flow at a driving point one gives the relationship between the variance of power mean power flow and the variances of force and velocity at a driving point another equation shows the mean power transferred for wide band random force is equal to the value of the impulse response function at zero time multiplied by the mean square value of the driving force

on entropy consistency of large time step schemes i the godunov and glimm schemes this paper shows for scalar conservation laws with a convex flux function that the large time step approximation of weak solutions gives entropy solutions in the limit if the courant number is between tfrac 1 2 and 1 for flux functions with constant curvature monotonicity or monotone initial data the results extend to larger courant numbers a continuity argument gives this result also for the case of fluxes with almost constant curvature

the dirichlet problem for sublaplacians on nilpotent lie groups geometric criteria for regularity on etudie un critere de regularite geometrique pour un sous ensemble ouvert relativement compact u d un espace harmonique

schauder estimates for parabolic nondivergence operators of hormander type let x1 x2 xq be a system of real smooth vector fields satisfying hormander s rank condition in a bounded domain of rn let a aij t x i j 1q be a symmetric uniformly positive definite matrix of real functions defined in a domain u r for operators of kind h t i j 1qaij t x xixj i 1qbi t x xi c t x we prove local a priori estimates of schauder type in the natural parabolic ck u spaces defined by the vector fields xi and the distance induced by them namely for aij bi c ck u and u u we prove u ck 2 u c hu ck u u l u

a class of large time step godunov schemes for hyperbolic conservation laws and applications a large time step lts godunov scheme firstly proposed by leveque is further developed in the present work and applied to euler equations based on the analysis of the computational performances of leveque s linear approximation on wave interactions a multi wave approximation on rarefaction fan is proposed to avoid the occurrences of rarefaction shocks in computations the developed lts scheme is validated using 1 d test cases manifesting high resolution for discontinuities and the capability of maintaining computational stability when large cfl numbers are imposed the scheme is then extended to multidimensional problems using dimensional splitting technique the treatment of boundary condition for this multidimensional lts scheme is also proposed as for demonstration problems inviscid flows over naca0012 airfoil and onera m6 wing with given swept angle are simulated using the developed lts scheme the numerical results reveal the high resolution nature of the scheme where the shock can be captured within 1 2 grid points the resolution of the scheme would improve gradually along with the increasing of cfl number under an upper bound where the solution becomes severely oscillating across the shock computational efficiency comparisons show that the developed scheme is capable of reducing the computational time effectively with increasing the time step cfl number

lower bounds for densities of asian type stochastic differential equations abstract we obtain lower bounds for densities of solutions of certain hypoelliptic two dimensional stochastic differential equations where one of the components is the lebesgue integral of the other these results are non trivial extensions of previous work of the authors in particular these type of equations are linked to the so called asian option set up

stein weiss inequalities for the fractional integral operators in carnot groups and applications in this article we consider the fractional integral operator i on any carnot group x1d53e i e nilpotent stratified lie group in the weighted lebesgue spaces l p x x1d53e we establish stein weiss inequalities for i and obtain necessary and sufficient conditions on the parameters for the boundedness of the fractional integral operator i from the spaces l p x x1d53e to l q x x1d53e and from the spaces l 1 x x1d53e to the weak spaces wl q x x1d53e by using the stein weiss inequalities in the limiting case we prove that the modified fractional integral operator is bounded from the space l p x x1d53e to the weighted bounded mean oscillation bmo space bmo x x1d53e where q is the homogeneous dimension of x1d53e as applications of the properties of the fundamental solution of sub laplacian on x1d53e we prove two sobolev stein embedding theorems on weighted lebesgue and weighted besov spaces in the carnot group setting as another application we prove the boundedness of i from the weighted besov

analysis on nilpotent groups soit g un groupe de lie nilpotent reel simplement connexe et soit l son algebre de lie soient l 1 l et l k 1 l k l k 1 2 soit d d g d l k 1 kdim r l k l k 1 d est la dimension de dirichlet de g soit h un groupe nilpotent discret finiment genere on demontre des theoremes d analyse pour g

green functions for weighted subelliptic p laplace operator constructed by hormander s vector fields abstract this paper deals with the weighted subelliptic p laplace operator constructed by hormander s vector fields l p u d i v x a x x u x x u x p 2 2 a x x u x where u w 1 p u w 1 p q and a x is a bounded measurable and m m symmetric matrix satisfying 1 w x 2 p 2 a x w x 2 p 2 r m w x a p we first prove existence of the modified green function for l p by virtue of minty browder theorem and then existence of the green function for l p by checking the convergence of sequence of modified green functions next we derive upper bounds of the modified green function for l p by establishing the interpolation inequality in the weighted weak l p spaces finally the bounds of the green function for l p are also obtained by virtue of results for the modified green function and the compact weighted embedding theorem

large time step shock capturing techniques for scalar conservation laws for a scalar conservation law u t f u x with f of constant sign the first order upwind difference scheme is a special case of godonov s method the method is equivalent to solving a sequence of riemann problems at each step and averaging the resulting solution over each cell in order to obtain the numerical solution at the next time level the difference scheme is stable and the solutions to the associated sequence of riemann problems do not interact provided the courant number nu is less than 1 by allowing and explicitly handling such interactions it is possible to obtain a generalized method which is stable for nu much larger than 1 in many cases the resulting solution is considerably more accurate than solutions obtained by other numerical methods in particular shocks can be correctly computed with virtually no smearing the generalized method is rather unorthodox and still has some problems associated with it nonetheless preliminary results are quite encouraging

the dirichlet problems for a class of semilinear sub elliptic equations where x x1 xm is a system of real smooth vector elds de ned in an open domain m rn n 2 is a bounded open subdomain of m with smooth c x c0 0 x j denote the adjoint of xj we assume that the system of vector elds x x1 xm satis es the following h ormander s condition x1 xm together with their commutators x x 1 x s 1 x s up to some xed length r span the tangent space at each point of m we have the following theorem

on entropy consistency of large time step schemes ii approximate riemann solvers it is shown that for scalar conservation laws with a convex flux function any sequence of approximate solutions constructed by large time step schemes using approximate riemann solvers as a building block gives the unique entropy solution in the limit of decreasing mesh size if the courant number is less than 1 when the curvature of the flux function is nearly constant the above results may be extended to courant numbers slightly larger than 1

boundary behavior of functions holomorphic in domains of finite type abstract we study several notions of distance and ball on the boundary of domains of finite type in cn we use these notions to develop a theory of maximal functions and area integrals for functions holomorphic in such domains