Propagation of Singularities for Solutions to Hamilton-Jacobi Equations
Vortragende: Prof. Dr. Piermarco Cannarsa, Univ. of Roma Tor Vergata, President of UMI
Veranstalter: Enrique Zuazua
The study of the structural properties of the set of points at which the viscosity solution of a first order Hamilton-Jacobi equation fails to be differentiable—in short, the singular set—started with the paper [On the singularities of viscosity solutions to Hamilton-Jacobi-Bellman equations, Indiana Univ. Math. J. 36 (1987), pp.501-524] by Mete Soner and myself. These thirty years have registered enormous progress in the comprehension of the way how singularities propagate: we have developed a fine measure theoretical analysis of the singular set, we can describe singular dynamics by generalised characteristics, and we have even found deep topological applications to the structure of the cut locus on a Riemannian manifold. In this talk, I will revisit the milestones of the theory and discuss possible developments and open problems.