*Published Paper*

**Inserted:** 13 aug 2016

**Last Updated:** 7 oct 2019

**Journal:** Arch. Ration. Mech. Anal.

**Year:** 2017

**Abstract:**

We prove that if $u$ is the entropy solution to a scalar conservation law in one space dimension, then the entropy dissipation is a measure concentrated on countably many Lipschitz curves. This result is a consequence of a detailed analysis of the structure of the characteristics.

In particular the characteristic curves are segments outside a countably 1-rectifiable set and the left and right traces of the solution exist in a $C^0$-sense up to the degeneracy due to the segments where $f''=0$.

We prove also that the initial data is taken in a suitably strong sense and we give some counterexamples which show that these results are sharp.

**Download:**