Event Detail

Event Type: 
Department Colloquium
Date/Time: 
Monday, March 4, 2019 - 16:00 to 16:50
Location: 
KIDD 364

Speaker Info

Institution: 
Western Washington University
Abstract: 

The study of one of the most renowned examples of free boundary problems, the classical obstacle problem, began in the 60’s with the pioneering works of G. Stampacchia, H. Lewy and J. L. Lions. During the past five decades, it has led to beautiful and deep developments in the calculus of variations and geometric partial differential equations. One of its crowning achievements has been the development, due to L. Caffarelli, of the theory of free boundaries. Nowadays the obstacle problem continues to offer many challenges and its study is as active as ever. In particular, over the past years there has been some interesting progress the thin obstacle problem, also called Signorini problem. In this talk, I will overview the obstacle problem and describe a few methods used to tackle two fundamental questions: what is the optimal regularity of the solution, and what can be said about the free boundary.

This is based on joint work with Nicola Garofalo and Arshak Petrosyan.