Restriction of viscosity solutions of the Hamilton-Jacobi equation to a submanifold M of \mathbb{R}^{d}

Abstract

We show in this article in what sense viscosity solutions of the Hamilton-Jacobi equation can be restricted to a submanifold M of \mathbb{R}^{d}. We treat in this article the case of M\times\mathbb{R}^{d} being invariant by the Hamiltonian vector field.