Calculus of Variations and Geometric Measure Theory

E. Marconi

On the structure of weak solutions to scalar conservation laws with finite entropy production

created by marconi on 16 Sep 2019
modified on 13 Sep 2021


Accepted Paper

Inserted: 16 sep 2019
Last Updated: 13 sep 2021

Journal: Calc. Var. PDEs
Year: 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.