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.File in questo prodotto:
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