Inserted: 16 sep 2019
Last Updated: 16 sep 2019
We consider weak solutions $u$ with finite entropy production to scalar conservation laws in $d$-space dimensions. Building on the kinetic formulation we prove under suitable nonlinearity assumption on the flux $f$ that the set of non Lebesgue points of $u$ has Hausdorff dimension at most $d$. A notion of Lagrangian representation for this class of solutions is introduced and this allows for a new interpretation of the entropy dissipation measure.