On a free boundary problem and minimal surfaces

Kelei Wang; Juncheng Wei; Yong Liu

doi:10.1016/j.anihpc.2017.09.005

JournalsaihpcVol. 35, No. 4pp. 993–1017

On a free boundary problem and minimal surfaces

Kelei Wang
School of Mathematics and Statistics, Wuhan University, China
- MathSciNet
- zbMATH Open
Juncheng Wei
Department of Mathematics, University of British Columbia, Vancouver, B.C., V6T 1Z2, Canada
Yong Liu
School of Mathematics and Physics, North China Electric Power University, Beijing, China
- MathSciNet
- zbMATH Open

Download PDF

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 8, using variational arguments, we also obtain solutions which are global minimizers of the corresponding energy functional. This shows that the theorem of Valdinoci et al. [41,42] is optimal.

Cite this article

Kelei Wang, Juncheng Wei, Yong Liu, On a free boundary problem and minimal surfaces. Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018), no. 4, pp. 993–1017

DOI 10.1016/J.ANIHPC.2017.09.005