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.

%I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/35209 %1 35508 %2 Mathematics %# MAT/05 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2016-09-06T09:18:03Z No. of bitstreams: 1 1608.02811v1.pdf: 591028 bytes, checksum: 069b218b01f350df6db7904e245ef701 (MD5)