Calculus of Variations and Geometric Measure Theory

S. Bianchini - C. De Lellis - R. Robyr

SBV regularity for Hamilton-Jacobi equations in R^n

created by delellis on 06 May 2011
modified on 02 Jul 2013


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

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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 $SBV_{loc}(\Omega)$.