Minimizers of a free boundary problem on three-dimensional cones

01/06/2021

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by   Mark Allen, et al.

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We consider a free boundary problem on three-dimensional cones depending on a parameter c and study when the free boundary is allowed to pass through the vertex of the cone. Combining analysis and computer-assisted proof, we show that when c is less than 4.3, the free boundary may pass through the vertex of the cone.