a viscosity solutions approach to shape from shading the problem of recovering a lambertian surface from a single two dimensional image may be written as a first order nonlinear equation which presents the disadvantage of having several continuous and even smooth solutions a new approach based on hamilton jacobi bellman equations and viscosity solutions theories enables one to study non uniqueness phenomenon and thus to characterize the surface among the various solutions a consistent and monotone scheme approximating the surface is constructed thanks to the dynamic programming principle and numerical results are presented

irreducible characters of general linear superalgebra and super duality we develop a new method to solve the irreducible character problem for a wide class of modules over the general linear superalgebra including all the finite dimensional modules by directly relating the problem to the classical kazhdan lusztig theory furthermore we prove that certain parabolic bgg categories over the general linear algebra and over the general linear superalgebra are equivalent we also verify a parabolic version of a conjecture of brundan on the irreducible characters in the bgg category of the general linear superalgebra

approximation schemes for viscosity solutions of hamilton jacobi equations abstract equations of hamilton jacobi type arise in many areas of applications including the calculus of variations control theory and differential games recently m g crandall and p l lions established the correct notion of generalized solutions for these equations this article discusses the convergence of general approximation schemes to this solution and gives under certain hypotheses explicit error estimates these results are then applied to obtain various representations as limits of solutions of general explicit and implicit finite difference schemes with error estimates

viscosity solutions for weakly coupled systems of first order partial differential equations abstract we consider viscosity solutions for weakly coupled systems of first order partial differential equations and apply these existence and uniqueness results to examples involving random evolutions

oscillation criteria for certain nonlinear differential equations we present new oscillation criteria for certain classes of second order nonlinear differential equations and delay differential equations obtained by using an integral averaging technique our theorems complement a number of existing results and handle the cases which are not covered by known criteria

howe duality and combinatorial character formula for orthosymplectic lie superalgebras we study the howe dualities involving the reductive dual pairs o d spo 2m 2n and sp d osp 2m 2n on the super symmetric tensor of cd cm n we obtain complete decompositions of this space with respect to their respective joint actions we also use these dualities to derive a character formula for these irreducible representations of spo 2m 2n and osp 2m 2n that appear in these decompositions

kostant homology formulas for oscillator modules of lie superalgebras abstract we provide a systematic approach to obtain formulas for characters and kostant u homology groups of the oscillator modules of the finite dimensional general linear and ortho symplectic superalgebras via howe dualities for infinite dimensional lie algebras specializing these lie superalgebras to lie algebras we recover in a new way formulas for kostant homology groups of unitarizable highest weight representations of hermitian symmetric pairs in addition two new reductive dual pairs related to the above mentioned u homology computation are worked out

optimal switching for ordinary differential equations we consider the problem of controlling an ordinary differential equation subject to positive switching costs and show in particular that the value functions form the viscosity solution cf 6 7 of the dynamic programming quasi variational inequalities this interpretation allows for a rigorous application of various dynamic programming techniques

on hopf s formulas for solutions of hamilton jacobi equations soit h r n r on considere l equation de hamilton jacobi u t h du 0 dans r n 1 r n 0 on etudie les proprietes des formules de hopf pour les solutions

a viscosity solution approach to the asymptotic analysis of queueing systems we consider a system of several interconnected queues with a single class of customers and model the state xt of the system as a jump markov process the problem of interest is to estimate the large deviations behavior of the rescaled system xt ext s corresponding to large time and large excursions of the original unscaled system the techniques employed are those of the theory of viscosity solutions to hamilton jacobi equations from the point of view of large deviation theory the interesting new problem here is the treatment of the process when one or more of the queues are nearly empty since an abrupt change in the jump measure occurs from the point of view of viscosity solutions the discontinuity of the jump measure leads to nonlinear boundary conditions on domains with corners for the associated partial differential equations much of the paper is devoted to proving uniqueness of viscosity solutions for these equations and these sections are of independent interest while our use of test functions in proving the uniqueness is an adaptation of the usual technique the construction of the test functions themselves via the legendre transform is new we obtain a representation for the solution of the equation in terms of a nonstandard optimal control problem which suggests the correct integrand in the large deviation rate functional since it is the treatment of the effects due to the boundaries that is novel we devote the majority of the paper to the detailed development of a simple two dimensional system that exhibits all the essential new features however the arguments may be applied to nueueing systems that are considerably more general and we attempt to indicate this generality as well

regular kac moody superalgebras and integrable highest weight modules we define regular kac moody superalgebras and classify them using integrable modules we give conditions for irreducible highest weight modules of regular kac moody superalgebras to be integrable this paper is a major part of the proof for the classification of finite growth contragredient lie superalgebras

oscillation criteria for linear matrix hamiltonian systems abstract in this paper we present oscillation criteria in terms of the coefficient functions for the matrix linear hamiltonian system u a x u b x v v c x u a x v under the hypothesis h a x b x b x 0 and c x c x are n n matrices of real valued continuous functions on the interval i a a these criteria generalize earlier results due to etgen and pawlowski 1976 erbe qingkai kong and shigui ruan 1993 and fanwei meng jizhong wang and zhaowen zheng 1998 for the system p x u q x u 0 or its special cases

weighted means and oscillation conditions for second order matrix differential equations on considere le systeme d equations differentielles d ordre 2 p t y t q t y t 0 pour t 0 ou p et q sont des matrices symetriques n n reelles sur 0 et y un vecteur colonne on suppose que p t est definie positive pour tout t tel que p t 1 on donne des conditions d oscillations

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

hamilton jacobi equations in infinite dimensions i uniqueness of viscosity solutions soient un espace de banach v son dual v et des solutions d une equation h x u du 0 dans etablies dans un sous ensemble de v h v r v r est continue on demontre que des solutions classiques sont determinees de facon unique par leurs valeurs limites on montre que l extension de la notion de solutions viscosite aux espaces de banach reussit dans des espaces munis de la propriete de radon nikodym

fully nonlinear neumann type boundary conditions for first order hamilton jacobi equations we consider problems of the following type h x u u 0 in where is a smooth bounded open set in r n u is a scalar function from into r u denotes its frechet differential at x and h is a given continuous function on xr r n this equation is nothing but a general form of the classical first order hamilton jacobi equation in order to investigate existence and uniqueness questions the equation has to be complemented with a boundary condition on or on a part of we consider here for reasons described below a fully nonlinear boundary condition of the form f x u u 0 on that we describe as being of the neumann type

kostant s formula for kac moody lie algebras abstract this paper is a generalization of h garland and j lepowsky s paper of 1976 let g a be the kac moody lie algebra defined by a symmetrizable generalized cartan matrix a m the irreducible highest weight module of g a with a dominant integral highest weight kostant s homology and cohomology formulas for the lie algebra g a and the module m are proved without assuming that the reductive part of the parabolic subalgebra of g a is of finite type a resolution of m is constructed for any j the jth term of the resolution has a filtration such that all the factors of the filtration are generalized verma modules of the form vm w p p where w ranges over a certain subset of the weyl group of g a

viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions part i the case of bounded stochastic evolutions on etudie des equations elliptiques degenerees d ordre 2 non lineaires de la forme f d 2 u du u x 0 dans h ou h est un espace de hilbert separable x un point generique dans h u une fonction de h r

oscillation of self adjoint linear matrix hamiltonian systems abstract by means of monotone functionals defined on suitable matrix spaces and new methods oscillation criteria for self adjoint linear hamiltonian matrix system of the form x x a x x x b x y x y x c x x x a x y x are obtained there results are sharper than some previous results even for self adjoint second order matrix differential systems in particular our theorems are generalizations and improvements of many existing results including those obtained by sun j math anal appl 279 2003 651 658

remarks on hamilton jacobi equations with measurable time dependent hamiltonians on considere les equations de hamilton jacobi de la forme suivante u t h x t u u 0 dans r n 0 t ou h x t s p est continu en x s p et mesurable en t on considere une extension de la notion de solution viscosite au cas de h mesurable dependant du temps

viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions iii uniqueness of viscosity solutions for general second order equations we prove here the uniqueness and existence of viscosity solutions for a general class of fully nonlinear second order equations in an infinite dimensional hilbert space the uniqueness is proved using the so called inf and sup convolutions which allow some reduction to finite dimensional problems

interval oscillation criteria for second order nonlinear differential equations with damping new oscillation criteria are established for the nonlinear damped differential equation ry py qf y 0 that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t0 rather than on the whole half line our results are sharper than some previous results and extend and improve the recent interval criteria of kong and huang and can be applied to extreme cases such as t0 q s ds in particular several examples that dwell upon the sharp conditions of our results are also included

a regularity result for viscosity solutions of hamilton jacobi equations in one space dimension on demontre que dans le cas particulier d un probleme stationnaire a une dimension sous des hypotheses tres generales les solutions viscosite continues de lipschitz ont des derivees a droite et a gauche en chaque point

viscosity solutions of hamilton jacobi equations with unbounded nonlinear terms abstract the aim of this paper is to introduce a new definition of viscosity solutions for hamilton jacobi equations in infinite dimensions with unbounded nonlinear terms we prove existence and uniqueness results under usual assumptions regarding the bounded part of the hamiltonian

integrable highest weight modules over affine superalgebras and appell s function we classify integrable irreducible highest weight representations of non twisted affine lie superalgebras we give a free field construction in the level 1 case the analysis of this construction shows in particular that in the simplest case of the sl 2 1 level 1 affine superalgebra the characters are expressed in terms of the appell elliptic function our results demonstrate that the representation theory of affine lie superalgebras is quite different from that of affine lie algebras

interval oscillation criteria related to integral averaging technique for certain nonlinear differential equations abstract we present new interval oscillation criteria related to integral averaging technique for certain classes of second order nonlinear differential equations that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t 0 rather than on the whole half line our results are sharper than some previous results and handle the cases which are not covered by known criteria in particular several examples that dwell upon the sharp conditions of our results are also included

super duality and irreducible characters of ortho symplectic lie superalgebras we formulate and establish a super duality which connects parabolic categories o for the ortho symplectic lie superalgebras and classical lie algebras of bcd types this provides a complete and conceptual solution of the irreducible character problem for the ortho symplectic lie superalgebras in a parabolic category o which includes all finite dimensional irreducible modules in terms of classical kazhdan lusztig polynomials

riccati techniques and variational principles in oscillation theory for linear systems on etablit des conditions suffisantes pour que toutes les solutions soient oscillatoires on utilise les techniques de riccati et les principes variationnels

irreducible representations of the exceptional lie superalgebras d 2 1 α the shift operator technique is used to give a complete analysis of all finite and infinite dimensional irreducible representations of the exceptional lie superalgebrasd 2 1 for all cases the star or grade star conditions for the algebra are investigated among the finite dimensional representations there are no star and only a few grade star representations but an infinite class of infinite dimensional star representations is found explicit expressions are given for the doublet representation of d 2 1 the one missing label problem d 2 1 su 2 su 2 su 2 is discussed in detail and solved explicitly

kinetic decomposition for singularly perturbed higher order partial differential equations abstract in this paper we consider singularly perturbed higher order partial differential equations we establish the condition under which the approximate solutions converge in a strong topology to the entropy solution of a scalar conservation laws using methodology developed in hwang and tzavaras comm partial differential equations 27 2002 1229 first we obtain the approximate transport equation for the given dispersive equations then using the averaging lemma we obtain the convergence

oscillation theorems for certain second order self adjoint matrix differential systems abstract by means of generalized averaging pair technique and riccati transformation method oscillation criteria for self adjoint differential matrix system of the form r t p t x t p t p t x t q t f x t g x t 0 are obtained this paper generalizes and improves the existing results including those obtained by yang 2002 li and agarwal 2000 and rogovchenko 1999

revisiting wall heating the results of computing a shock reflection are found to strongly depend on the chosen coordinate system lagrangian or eulerian this is seen by comparing the amount of wall heating associated with the solutions to noh s shock reflection problem computed in each reference frame here an explanation is offered that places a greater burden on the role of phase error or effective wave speed in producing this effect the reason for the greater difficulties in the lagrangian frame are the non uniformity of the mass coordinates in a converging geometry this produces a non steady state discrete shock profile

integral averaging techniques for the oscillation of second order nonlinear differential equations abstract in this paper we enlist some known and establish some new oscillation criteria for the second order nonlinear differential equations of the form if a t x t t su p t t q t f x t 0 where the coefficients p t and q t are not assumed to be nonnegative for all large values of t these criteria are obtained by using integral averaging techniques and can be applied to some special cases where other classical oscillation results are not applicable a systematic study is attempted to extend improve and correlate a number of existing results

an asymptotic formula for solutions of hamilton jacobi bellman equations on demontre que la solution de l equation de hamilton jacobi bellman converge exponentiellement vers 0 quand e 0 avec un taux de decroissance i x 0 1 e et on donne une formule de representation pour i x

on existence and uniqueness of solutions of hamilton jacobi equations abstract the theory of scalar first order nonlinear partial differential equations has been enjoying a rapid development in the last few years this development occurred because the authors established uniqueness criteria for generalized solutions called viscosity solutions which correctly identify the solutions sought in areas of application including control theory differential games and the calculus of variations the concept of viscosity solutions is relatively easy to work with and many formally heuristic or difficult proofs have been made rigorous or simple using this concept a feedback process has begun and the experience recently gained in working with viscosity solution has suggested new existence and uniqueness results the current paper continues this interaction by establishing new existence ane uniqueness results in a natural generality suggested by earlier proofs it is also felt that the presentation of the comparison results which imply uniqueness continuous dependence and are used to estimate moduli of continuity has something to offer over earlier presentations in special cases author

the necessary conditions for optimal control in hilbert spaces obtention du principe maximum de pontryagin pour une classe generale de problemes de commande de type lagragien afin qu associe avec un ensemble de conditions necessaires une commande soit satisfaite le principe est demontre en utilisant la programmation dynamique et l equation resultante d hamilton jacobi bellman de dimension finie

the boundary value problem for quasilinear degenerate and singular elliptic systems abstract in this paper using the contraction mapping principle and the shooting method we obtain the existence and uniqueness of the local solutions and the global solutions to a class of quasilinear degenerate elliptic systems with the p laplacian like as its principal and with singularity on the boundary we also obtain the continuous dependence of the solution on the boundary data two examples are given to illustrate the applications of the theorems

some properties of viscosity solutions of hamilton jacobi equations abstract recently m g crandall and p l lions introduced the notion of viscosity solutions of scalar nonlinear first order partial differential equations viscosity solutions need not be differentiable anywhere and thus are not sensitive to the classical problem of the crossing of characteristics the value of this concept is established by the fact that very general existence uniqueness and continuous dependence results hold for viscosity solutions of many problems arising in fields of application the notion of a viscosity solution admits several equivalent formulations here we look more closely at two of these equivalent criteria and exhibit their virtues by both proving several new facts and reproving various known results in a simpler manner moreover by forsaking technical generality we hereby provide a more congenial introduction to this subject than the original paper author