Orateur
Xavier Lamy
(Institut de Mathématiques de Toulouse)
Description
Among weak solutions of Burgers' equation, a single strictly convex entropy is sufficient to characterize the sign of all entropy productions. In particular, if that entropy production vanishes, then the solution must be continuous. It turns out that this fact can be interpreted as a regularity result for a degenerate elliptic equation in the plane, and generalized to prove partial regularity results for a large class of planar nonlinear equations $\mathrm{div}\: G(\nabla u)=0$ which are only qualitatively elliptic. This is joint work with Riccardo Tione.