Inserted: 13 aug 2016
Last Updated: 13 aug 2016
Journal: Discrete and Continuous Dynamical Systems. Series S
We prove that the entropy for an $L^\infty$-solution to a scalar conservation laws with continuous initial data is concentrated on a countably $1$-rectifiable set. To prove this result we introduce the notion of Lagrangian representation of the solution and give regularity estimates on the solution.
Keywords: shocks, concentration, Conservation laws, entropy solutions, Lagrangian representation