Published Paper
Inserted: 18 sep 2003
Last Updated: 25 oct 2005
Journal: ESAIM: Control Opt. Calc. Var.
Volume: 11
Pages: 229-251
Year: 2005
Abstract:
We consider an Hamilton-Jacobi equation of the form $H(x,Du)=0$ in $A$, where $A$ is a subset of $R^N$ and $H(x,p)$ is Borel measurable and quasi-convex in $p$. The notion of Monge solution, introduced by Newcomb and Su, is adapted to this setting making use of suitable metric devices. We establish the comparison principle for Monge sub and supersolution, existence and uniqueness for the above equation coupled with Dirichlet boundary conditions, and a stability result. The relation among Monge and Lipschitz subsolutions is also discussed.
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