Harmonic Maps with Free Boundary: Regularity, Singularity Formation and Geometric Applications

Explore recent advancements in harmonic maps with free boundary in this 57-minute lecture by Yannick Sire at ICBS2024. Delve into the existence, regularity, and parabolic blow-up of harmonic map systems between smooth manifolds. Examine both elliptic and parabolic problems, and discover how recent progress in pseudo-differential equation regularity theory provides a fresh perspective on constructing blow-up solutions for heat flow. Gain insights into geometric applications, particularly focusing on the Steklov problem. Enhance your understanding of this complex mathematical topic and its implications in various fields of study.