Variational Problems on Arbitrary Sets
Dr. Kevin Luli , University of California, Davis
Abstract: Let E be an arbitrary subset of Rn. Given functions f : E ! R and
g : Rn ! R, the classical obstacle problem asks for a minimizer of the energy
functional E(F) =
R
Rn jrFj2 subject to the following two constraints: (1) F = f
on E and (2) F g on Rn. In this talk, we will discuss how to use extension theory
to construct the 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.
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