Minimizers of a free boundary problem on three-dimensional cones

Published 6 Jan 2021 in math.AP, cs.NA, and math.NA | (2101.02262v2)

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.