PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Carina Curto.

Title:Special Time - Wed @ 2:30pm: Analytic Foundations for Kimura Diffusion Equations
Seminar:Mathematical Biology Colloquium
Speaker:Charles Epstein, University of Pennsylvania (host: Leonid Berlyand)
Abstract:
We discuss the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in Population Biology. Using techniques pioneered by J. Moser, and extended and refined by L. Saloff-Coste, Grigor’yan, and Sturm, we show that weak solutions to the parabolic problem defined by a sub-class of these operators, which consists of those that can be defined by Dirichlet forms and have non- vanishing transverse vector field, satisfy a Harnack inequality. This allows us to conclude that the solutions to these equations belong, for positive times, to the natural anisotropic Holder spaces, and also leads to upper and, in some cases, lower bounds for the heat kernels of these operators.

Room Reservation Information

Room Number:MB114
Date:02 / 04 / 2015
Time:02:30pm - 03:20pm