## Gamma-Convergence and Saddle Points

- Date: 05/09/2007

Robert Jerrard (University of Toronto)

University of British Columbia

We prove a theorem asserting, roughly speaking, that if a sequence of

functionals converges to a limiting functional (in the sense of

Gamma-convergence, a natural and widely-used notion in the calculus of

variations), and if the limiting functional has a nondegenerate

critical point, then the approximating functionals have an associated

critical point. This is an analog for saddle points of a theorem about

local minimizers, due to Kohn and Sternberg, that has been known for

about 20 years. We apply the theorem to prove the existence of certain

solutions of Ginzburg-Landau equations. This is joint work with Peter

Sternberg

UBC Mathematics Department Colloquium Hosted by PIMS-UBC 2007