English

Free boundary on a cone

Analysis of PDEs 2013-01-28 v1

Abstract

We study two phase problems posed over a two dimensional cone generated by a smooth curve γ\gamma on the unit sphere. We show that when length(γ)<2πlength(\gamma)<2\pi the free boundary avoids the vertex of the cone. When length(γ)2πlength(\gamma) \geq 2\pi we provide examples of minimizers such that the vertex belongs to the free boundary.

Keywords

Cite

@article{arxiv.1301.6047,
  title  = {Free boundary on a cone},
  author = {Mark Allen and Hector Chang Lara},
  journal= {arXiv preprint arXiv:1301.6047},
  year   = {2013}
}
R2 v1 2026-06-21T23:15:18.203Z