We considers a non-convex first order Hamilton-Jacobi equation, with a non-homogeneous Dirichlet boundary condition in a bounded region. The boundary datum is Lipschitz continuous, and the existence of (Lipschitz continuous in the interior and continuous on the boundary) viscosity solutions is discussed. It is proved that a compatibility condition is sufficient for the existence of viscosity solutions. This condition is expressed in a geometric way, involving the inward normal (where it is uniquely defined) and the Hamiltonian.

Sufficient conditions for the existence of viscosity solutions for nonconvex Hamiltonians

PISANTE, Giovanni
2004

Abstract

We considers a non-convex first order Hamilton-Jacobi equation, with a non-homogeneous Dirichlet boundary condition in a bounded region. The boundary datum is Lipschitz continuous, and the existence of (Lipschitz continuous in the interior and continuous on the boundary) viscosity solutions is discussed. It is proved that a compatibility condition is sufficient for the existence of viscosity solutions. This condition is expressed in a geometric way, involving the inward normal (where it is uniquely defined) and the Hamiltonian.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11591/205104
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