Variational Problems on Arbitrary Sets
Time: 2018-12-03
Published By: He Liu
Speaker(s): Garving Luli (UC Davis)
Time: 15:00-17:00 December 11, 2018
Venue: Room 29, Quan Zhai, BICMR
Let E be an arbitrary subset of R^n. Given real valued functions f defined on E and g defined on R^n, the classical Obstacle Problem asks for a minimizer of the Dirichlet energy subject to the following two constraints: (1) F = f on E and (2) F \geq g on R^n. In this talk, we will discuss how to use extension theory to construct (almost) solutions directly. We will also explain several recent results that will help lay the foundation for building a complete theory revolving around the belief that any variational problems that can be solved using PDE theory can also be dealt with using extension theory.
