Calculus of Variations and Geometric Measure Theory

S. Bianchini - E. Marconi

A Lagrangian approach to scalar conservation laws

created by marconi on 06 Dec 2016



Inserted: 6 dec 2016
Last Updated: 6 dec 2016

Year: 2016


We consider the entropy solution u of a scalar conservation law in one-space di- mension. In particular we prove that the entropy dissipation is a measure concen- trated on countably many Lipschitz curves. This follows from a detailed analysis of the structure of the characteristics. We will introduce a few notions of Lagrangian representations and we prove that characteristics are segments outside a countably 1-rectifiable set.