On the Structure of L∞ -Entropy Solutions to Scalar Conservation Laws in One-Space Dimension

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