SBV Regularity for Hamilton–Jacobi Equations in Rn
Stefano Bianchini, Camillo De Lellis and Roger Robyr
Abstract: In this paper we study the regularity of viscosity solutions to the following Hamilton–Jacobi equations
∂tu+H(Dxu) = 0 in Ω ⊂ R×Rn .
In particular, under the assumption that the Hamiltonian H ∈ C2(Rn) is uniformly convex, we prove that Dxu and ∂tu belong to the class SBVloc(Ω).