Minimizers of a free boundary problem on three-dimensional cones. (January 2023) - Allen, Mark; Barker, Blake; Gardiner, Jason; Zhao, Mingyan
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 ≤ 0 . 43 the free boundary may pass through the vertex of the cone.