TY - JOUR T1 - SBV regularity for Hamilton-Jacobi equations in R^n JF - Arch. Rational Mech. Anal. 200 (2011) 1003-1021 Y1 - 2011 A1 - Stefano Bianchini A1 - Camillo De Lellis A1 - Roger Robyr AB -

In this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$ \partial_t u + H(D_{x} u)=0 \qquad \textrm{in}\quad \Omega\subset \mathbb{R}\times \mathbb{R}^{n} . $$ 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 $SBV_{loc}(\Omega)$.

PB - Springer UR - http://hdl.handle.net/1963/4911 U1 - 4695 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER -