%0 Journal Article %J Arch. Rational Mech. Anal. 200 (2011) 1003-1021 %D 2011 %T SBV regularity for Hamilton-Jacobi equations in R^n %A Stefano Bianchini %A Camillo De Lellis %A Roger Robyr %X

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 $SBV_{loc}(\Omega)$.

%B Arch. Rational Mech. Anal. 200 (2011) 1003-1021 %I Springer %G en %U http://hdl.handle.net/1963/4911 %1 4695 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-25T10:18:41Z\\nNo. of bitstreams: 1\\n1002.4087v1.pdf: 272486 bytes, checksum: 551dab603b0252ec9c22800b33360d02 (MD5) %R 10.1007/s00205-010-0381-z