Abstract: Let $M$ and $N$ be two Riemannian manifolds. We will look at the set of $W^{1,p}$ mappings $u:M \to N$ having a fixed trace on boundary of $M$. Our goal is to study the map that minimizes the $L_p$ norm of the gradient, $\int |D u|^p$, among all such mappings. Hardt and Lin (1987) proved that a minimizer is locally Holder continuous outside a set of measure zero. In this talk, we will analyze the key steps involved in the proof of the result and do a quick introduction to the generalization of the result in fractional Sobolev spaces. This is based on joint work with Katarzyna Mazowiecka and Armin Schikorra.

Friday, September 6, 2024 - 14:00 to 15:00

Thackeray 703