Optimal Regularizing Effect for Scalar Conservation Laws
  We investigate the regularity of bounded weak solutions of scalar conservation laws with uniformly convex flux in space dimension one, satisfying an entropy condition with entropy production term that is a signed Radon measure. The proof is based on the kinetic formulation of scalar conservation laws and on an interaction estimate in physical space. 
Fran\c{c}ois Golse, Beno\^it Perthame
math.AP