00804nas a2200133 4500008004100000245005600041210005400097260001300151520040700164100002300571700002300594700001700617856003600634 2011 en d00aSBV regularity for Hamilton-Jacobi equations in R^n0 aSBV regularity for HamiltonJacobi equations in Rn bSpringer3 a
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 $SBV_{loc}(\Omega)$.
1 aBianchini, Stefano1 aDe Lellis, Camillo1 aRobyr, Roger uhttp://hdl.handle.net/1963/4911