%0 Report
%D 2016
%T On the structure of $L^\infty$-entropy solutions to scalar conservation laws in one-space dimension
%A Stefano Bianchini
%A Elio Marconi
%X 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
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