On a free boundary problem and minimal surfaces |
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| Authors: | Yong Liu Kelei Wang Juncheng Wei |
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| Affiliation: | 1. School of Mathematics and Physics, North China Electric Power University, Beijing, China;2. School of Mathematics and Statistics, Wuhan University, China;3. Department of Mathematics, University of British Columbia, Vancouver, B.C., V6T 1Z2, Canada |
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| 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. |
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| Keywords: | Free boundary problems Minimal surfaces Global minimizers Allen–Cahn equation Reduction method |
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