Bounded weak solutions to degenerate elliptic PDE with data in Orlicz spaces

When

October 20, 2023 | 2:30 p.m. – 3:30 p.m.
Refreshments provided

Where

University Hall 4002

Speaker

David Cruz-Uribe, University of Alabama

Abstract

In the study of the regularity of elliptic PDEs, a crucial step is a classical result due to Trudinger (among others): if the initial data is in a sufficiently good space (that is, in $L^p$ for $p$ sufficiently large), then the solution is bounded. This result has been generalized in various directions, including to degenerate (that is, not uniformly elliptic) partial differential equations. As part of a long term project with Scott Rodney at Cape Breton University to systematically study degenerate equations, we have proved a generalization of Trudinger’s result that holds for a very broad class of degenerate elliptic PDEs. We will discuss the formulation and proof of this result, and give its connection to our larger project.