Geodesic
On a free boundary problem and minimal surfaces
Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 4, pp. 993-1017
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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.

DOI : 10.1016/j.anihpc.2017.09.005
Keywords: Free boundary problems, Minimal surfaces, Global minimizers, Allen–Cahn equation, Reduction method 
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Liu, Yong; Wang, Kelei; Wei, Juncheng. On a free boundary problem and minimal surfaces. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 4, pp. 993-1017. doi: 10.1016/j.anihpc.2017.09.005

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