Analysis Seminar: Xavier Lamy (Toulouse) — On relaxed harmonic maps with anisotropy

Consider maps $u:R^n\to R^k$ with values constrained in a fixed submanifold, and minimizing (locally) the energy $E(u)=\int W(
abla u)$. Here $W$ is a positive definite quadratic form on matrices. Compared to the isotropic case $W(
abla u)=|
abla u|^2$ this may look like a harmless generalization, but the regularity theory for general $W$'s is widely open. I will explain why, and describe results with Andres Contreras on a relaxed problem, where the manifold-valued constraint is replaced by an integral penalization.
Zoom link:
https://huji.zoom.us/j/87592809411?pwd=bm11clcycEI1RzF4c2svbDFaaEJ2Zz09

Date: 

Wed, 04/11/2020 - 12:00 to 13:00

Location: 

Zoom