# A note on admissible solutions of 1D scalar conservation laws and 2D Hamilton-Jacobi equations

Ambrosio, L; De Lellis, C (2004). A note on admissible solutions of 1D scalar conservation laws and 2D Hamilton-Jacobi equations. Journal of Hyperbolic Differential Equations, 1(4):813-826.

## Abstract

Let Ω⊂ℝ2 be an open set and f∈C2(ℝ) with f" > 0. In this note we prove that entropy solutions of Dtu+Dxf(u) = 0 belong to SBVloc(Ω). As a corollary we prove the same property for gradients of viscosity solutions of planar Hamilton–Jacobi PDEs with uniformly convex Hamiltonians.

## Abstract

Let Ω⊂ℝ2 be an open set and f∈C2(ℝ) with f" > 0. In this note we prove that entropy solutions of Dtu+Dxf(u) = 0 belong to SBVloc(Ω). As a corollary we prove the same property for gradients of viscosity solutions of planar Hamilton–Jacobi PDEs with uniformly convex Hamiltonians.