Tuesday, February 18, 2014 - 3:05pm
1 hour (actually 50 minutes)
In a comparison theorem, one compares the solution of a given PDE to a solution of a second PDE where the data are "rearranged." In this talk, we begin by discussing some of the classical comparison results, starting with Talenti's Theorem. We then discuss Neumann comparison results, including a conjecture of Kawohl, and end with some new results in balls and shells involving cap symmetrization.