## 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

[

BibTeX]

*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.ch*delellis*

**Abstract:**

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