Speaker: Cristian Enache (American University of Sharjah) https://www.aus.edu/faculty/cristian-enache
Title: A survey on the maximum principle and its applications
Abstract:
In this talk we will survey some old and new results on the maximum principles (especially for for P-functions) and their applications to the study of partial differential equations. More precisely, we will show how one can employ the maximum principle in problems of physical or geometrical interest, in order to get the shape of some free boundaries, isoperimetric inequalities, symmetry results, convexity results and Liouville type results. In the first part of the talk we'll be mainly focused on some overdetermined problems, while in the second part of the talk we'll present some of our contributions to some Monge-Ampere type problems. Finally, we will discuss some open problems where the use of the maximum principle might be useful.
