Calculus of Variations and Geometric Measure Theory

E. Marconi

The rectifiability of the entropy defect measure for Burgers equation

created by marconi on 21 Apr 2020
modified on 17 May 2022


Accepted Paper

Inserted: 21 apr 2020
Last Updated: 17 may 2022

Journal: Journal of Functional Analysis
Year: 2020


We consider bounded weak solutions to the Burgers equation for which every entropy dissipation is representable by a measure and we prove that all these measures are concentrated on the graphs of countably many Lipschitz curves. The main tool is the Lagrangian representation, which is an extension of the method of characteristics to the non-smooth setting.