SBV regularity for Hamilton-Jacobi equations in ${\mathbb{R}}^n$

Abstract

In this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $${\partial }_{t}u+H(D_{x}u)=0\text{in}\Omega \subset \mathbb{R}\times {\mathbb{R}}^n.$$ In particular, under the assumption that the Hamiltonian $H\in C^2({\mathbb{R}}^n)$ is uniformly convex, we prove that $D_{x}u$ and ${\partial }_{t}u$ belong to the class $SB{V}_{loc}(\Omega )$.

15 pages

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