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Free boundary on a cone

By Mark Allen and Hector Chang Lara


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

Topics: Mathematics - Analysis of PDEs
Year: 2013
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