Special Session 149: Recent developments in Free Boundary Problems and Nonlinear PDEs

Fractional Parabolic Theory as a High-Dimensional Limit of Fractional Elliptic Theory
Mariana Smit Vega Garcia
Western Washington University
USA
Co-Author(s):    Blair Davey
Abstract:
Since elliptic PDE theory can be seen as a steady-state version of parabolic PDE theory, if a parabolic estimate holds, then by eliminating the time parameter, one can obtain an underlying elliptic statement. Producing a parabolic statement from an elliptic statement, on the other hand, is not as straightforward. In this talk, we will discuss how a high-dimensional limiting technique can be used to prove theorems about solutions to the fractional heat equation from their elliptic counterparts.