On optimal regularity estimates for finite-entropy solutions of scalar conservation laws - Lamy, Xavier; Lorent, Andrew; Peng, Guanying (Comptes Rendus. Mathématique)
We consider finite-entropy solutions of scalar conservation laws $u_t +a(u)_x =0$, that is, bounded weak solutions whose entropy productions are locally finite Radon measures. Under the assumptions that the flux function $a$ is strictly convex (with possibly degenerate convexity) and $a^{′ ′ }$ forms a doubling measure, we obtain a characterization of finite-entropy solutions in terms of an optimal regularity estimate involving a cost function first used by Golse and Perthame.