01088nas a2200121 4500008004100000245010400041210006900145260001000214520065000224100002300874700001800897856005100915 2016 en d00aOn the structure of $L^\infty$-entropy solutions to scalar conservation laws in one-space dimension0 astructure of Linftyentropy solutions to scalar conservation laws bSISSA3 aWe 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.1 aBianchini, Stefano1 aMarconi, Elio uhttp://urania.sissa.it/xmlui/handle/1963/35209