Hamilton-Jacobi equations on metric spaces and transport entropy inequalities

PDE Seminar
Tuesday, March 27, 2012 - 15:05
1 hour (actually 50 minutes)
Skiles 005
University of Paris, Nanterre
We will prove an Hopf-Lax-Oleinik formula for the solutions of some Hamilton-Jacobi equations on a general metric space. Then, we will present some consequences: in particular the equivalence of the log-Sobolev inequality and the hypercontractivity property of theHamilton-Jacobi "semi-group", (and if time allows) that Talagrand’s transport-entropy inequalities in metric space are characterizedin terms of log-Sobolev inequalities restricted to the class of c-convex functions (based on a paper in collaboration with N. Gozlan and P.M. Samson).