Uniqueness of Weak Solutions of the Plateau Flow
Analysis of PDEs
2023-03-23 v1 Differential Geometry
Abstract
In this paper, we study the uniqueness of weak solutions of the Plateau flow, which was first introduced by Wettstein as a half-Laplacian heat flow and recently studied by Struwe using alternative methods. This geometric gradient flow is of interest due to its links with free boundary minimal surfaces and the Plateau problem. We obtain uniqueness of weak solutions of this flow under a natural condition on the energy, which answers positively a question raised by Struwe.
Keywords
Cite
@article{arxiv.2303.12650,
title = {Uniqueness of Weak Solutions of the Plateau Flow},
author = {Christopher Wright},
journal= {arXiv preprint arXiv:2303.12650},
year = {2023}
}
Comments
10 pages