On a free boundary problem and minimal surfaces
Analysis of PDEs
2017-04-27 v1 Differential Geometry
Abstract
From minimal surfaces such as Simons' cone and catenoids, using refined Lyapunov-Schmidt reduction method, we construct new solutions for a free boundary problem whose free boundary has two components. In dimension , using variational arguments, we also obtain solutions which are global minimizers of the corresponding energy functional. This shows that Savin's theorem is optimal.
Cite
@article{arxiv.1704.07869,
title = {On a free boundary problem and minimal surfaces},
author = {Yong Liu and Kelei Wang and Juncheng Wei},
journal= {arXiv preprint arXiv:1704.07869},
year = {2017}
}
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34 pages