Reflection of Willmore surfaces with free boundaries

Abstract

We study immersed surfaces in ${\mathbb{R}}^3$ which are critical points of the Willmore functional under boundary constraints. The two cases considered are when the surface meets a plane orthogonally along the boundary, and when the boundary is contained in a line. In both cases we derive weak forms of the resulting free boundary conditions and prove regularity by reflection.

20 pages

References in corpus (1)

• A Resolution of the Poisson Problem for Elastic Plates