395 research outputs found
On a free boundary problem and minimal surfaces
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.Comment: 34 page
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