Published Paper
Inserted: 6 may 2011
Last Updated: 2 jul 2013
Journal: Arch. Ration. Mech. Anal.
Volume: 200
Number: 3
Pages: 1003-1021
Year: 2011
Notes:
For the update version and eventual errata see the webpage http:/www.math.uzh.chdelellis
Abstract:
In this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$ \partialt u + H(D{x} u)=0 \qquad \textrm{in } \Omega\subset \R\times \R{n}\, . $$ In particular, under the assumption that the Hamiltonian $H\in C^2(\R^n)$ is uniformly convex, we prove that $D_{x}u$ and $\partial_t u$ belong to the class $SBV_{loc}(\Omega)$.