Calculus of Variations and Geometric Measure Theory

G. Crasta - V. De Cicco - G. De Philippis - F. Ghiraldin

Structure of solutions of multidimensional conservation laws with discontinuous flux and applications to uniqueness

created by decicco on 03 Feb 2016
modified by dephilipp on 30 Oct 2017


Accepted Paper

Inserted: 3 feb 2016
Last Updated: 30 oct 2017

Journal: Arch. Ration. Mech. An.
Year: 2016

ArXiv: 1509.08273 PDF


We investigate the structure of solutions of conservation laws with discontinuous flux under quite general assumption on the flux. We show that any entropy solution admits traces on the discontinuity set of the coefficients and we use this to prove the validity of a generalized Kato inequality for any pair of solutions. Applications to uniqueness of solutions are then given.