Free boundary on a cone

preprint2013arXivOpen access

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

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Free boundary on a cone

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