Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Minimax Theory and its Applications 01 (2016), No. 1, 051--063Copyright Heldermann Verlag 2016 Representation of Viscosity Solutions of Hamilton-Jacobi Equations Emmanuel N. Barron Department of Mathematics and Statistics, Loyola University, Chicago, IL 60660, U.S.A. ebarron@luc.edu [Abstract-pdf] Hamilton Jacobi equations of the form $H(x,u,Du)=0$ are considered with $H(x,r,p)$ nondecreasing in $r$ and quasiconvex in $p$. A viscosity solution may be represented as the value function of a calculus of variations or control problem in $L^\infty$, i.e., as a minimax problem. For time dependent problems of the form $u_t+H(t,x,u,Du)=0$ we require that $H(t,x,r,p)$ is convex in $p$ and nondecreasing in $r$. The viscosity solution is then given as the value of an $L^\infty$ problem. Keywords: Quasiconvex, Hamilton-Jacobi, representation. MSC: 35F21, 49L25 [ Fulltext-pdf  (148  KB)] for subscribers only.