Fractional Parabolic Theory as a High-dimensional Limit of Fractional Elliptic Theory

Parallels between elliptic and parabolic theory of partial differential equations have long been explored. In particular, since elliptic theory can be seen as a steady-state version of parabolic theory, if a parabolic estimate holds, then by eliminating the time parameter, one can obtain the 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.

This is joint work with Blair Davey.