"Semiconcavity of solutions of Hamilton-Jacobi equations"
It is well known that nonlinear first order PDEs usually do not possessglobal smooth solutions, even if the data are smooth. Therefore, one has to consider suitable notions of generalized solutions, e.g. viscosity solutions, which are in general nondifferentiable. A regularity property that can often be proved in this context is semiconcavity, that is, the solution can be written as the sum of a concave function and a smooth one. In this talk we expose some semiconcavity results for the solutions of Hamilton-Jacobi equations, ranging from classical ones to some recent theorems concerning equations associated to optimal control problems with exit time.
TUESDAY, March 2, 2004