Fully non linear equations for nonlocal diffusions

July 15, 2009 University of Coimbra

Speaker: Luis Caffarelli (about)
Abstract: Fully non linear equations arise in optimal control and game theory, when one is able to optimize a (continuous) diffusion process (or has incomplete information about it). A complete theory of existence and regularity for these equations was developed in the eighties thanks to the remarkable contributions of Krylov and Safanov ( the Harnack inequality) and of Evans-Krylov (the Evans-Krylov regularity theorem) In a series of papers, in collaboration with Luis Silvestre, we developed the parallel theory in the case of discontinuous (Levy type) diffusion. I plan to present the main steps of the theory, and give an idea of our proof of the Evans Krylov theorem in this case.


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