SBV regularity for Hamilton-Jacobi equations in $\R^n$

Details SBV regularity for Hamilton-Jacobi equations in $\R^n$ SBV regularity for Hamilton-Jacobi equations in $\R^n$

2010-02-22

arxiv.org/abs/1002.4087v1

Mathematics

Analysis of PDEs

15 pages

Scientific paper

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 $SBV_{loc}(\Omega)$.

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