Representation of Viscosity Solutions of Hamilton-Jacobi Equations
Keywords:
Quasiconvex, Hamilton-Jacobi, representationAbstract
Hamilton Jacobi equations of the form H(x,u,Du) = 0 are considered with H(x,r,p) non decreasing 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∞, i.e., as a minimax problem. For
time dependent problems of the form ut + 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∞ problem.
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