On a free boundary problem and minimal surfaces

  • Kelei Wang

    School of Mathematics and Statistics, Wuhan University, China
  • 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


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