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arXiv · 2101.02262

Minimizers of a free boundary problem on three-dimensional cones

Mark Allen·Blake Barker·Jason Gardiner·Mingyan Zhao
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Abstract

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 0.43, the free boundary may pass through the vertex of the cone.

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Mark Allen, Blake Barker, Jason Gardiner, Mingyan Zhao. 2021-01-06. Minimizers of a free boundary problem on three-dimensional cones. https://arxiv.org/abs/2101.02262

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