10/24/2011

Charles Epstein
University of Pennsylvania

Existence and regularity for a class of degenerate diffusions arising in population genetics

Infinite population limits of standard Markov chain models lead to Markov processes on polyhedral domains that are formally generated by degenerate elliptic operators. These operators are characterized, in part, by the first order vanishing, along the boundary, of the coefficient of the second normal derivative term. This fact places these operators beyond those which have thus far been successfully analyzed using methods of geometric analysis. I will present an approach to these operators, which I have been pursuing with Rafe Mazzeo, based on an-isotropic Holder spaces, which leads to a rather complete existence, uniqueness and regularity theory.