Room P3.10, Mathematics Building

Diogo Oliveira e Silva, Hausdorff Center for Mathematics da Universidade de Bona
On extremizers for Fourier restriction inequalities

This talk will focus on extremizers for a family of Fourier restriction inequalities on planar curves. It turns out that, depending on whether or not a certain geometric condition related to the curvature is satisfied, extremizing sequences of nonnegative functions may or may not have a subsequence which converges to an extremizer. We hope to describe the method of proof, which is of concentration compactness flavor, in some detail. Tools include bilinear estimates, a variational calculation, a modification of the usual method of stationary phase and several explicit computations.