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

Wed, 04/11/202012:00-13:00
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.
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