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arxiv: 1410.7463 · v1 · pith:JCTGJAH3new · submitted 2014-10-28 · 🧮 math.AP

Some remarks on stability of cones for the one-phase free boundary problem

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keywords boundaryconesdimensionfreeone-phaseproblemcorollaryenergy
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We show that stable cones for the one-phase free boundary problem are hyperplanes in dimension $4$. As a corollary, both one and two-phase energy minimizing hypersurfaces are smooth in dimension $4$.

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