26 jan 2011
Dipartimento di Matematica - Sala Seminari - ore 17:00
ABSTRACT: In this second talk, we show that the entropy solution to the Cauchy problem, for small BV initial data and in the case of genuinely non-linear characteristic fields, belongs to SBV (joint work with S. Bianchini). This regularity was obtained first by Ambrosio and De Lellis in the case of a single equation with uniformly convex flux. Some years later it has been extended to scalar balance laws by Robyr, and recently to genuinely nonlinear Temple systems of balance laws by Ancona-Nguyen. An extension in more space dimensions has moreover been given by Bianchini-De Lellis-Robyr in the context of the Hamilton-Jacobi equation with uniformly convex Hamiltonian.