Minimizers of a free boundary problem on three-dimensional cones
Mark Allen, Blake Barker, Jason Gardiner, Mingyan Zhao
TL;DR
This paper investigates a free boundary problem on 3D cones, determining conditions under which the free boundary can pass through the cone's vertex, using analysis and computer-assisted proofs.
Contribution
It identifies a critical parameter value below which the free boundary can pass through the cone's vertex, combining analytical and computational methods.
Findings
Free boundary passes through the vertex when c < 0.43
Analysis and computer-assisted proof techniques are used
Provides a threshold parameter for boundary behavior
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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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Advanced Differential Equations and Dynamical Systems