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arXiv · 1711.08339

Free boundary problems involving singular weights

Jimmy Lamboley·Yannick Sire·Eduardo V. Teixeira
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Abstract

In this paper we initiate the investigation of free boundary minimization problems ruled by general singular operators with $A_2$ weights. We show existence and boundedness of minimizers. The key novelty is a sharp $C^{1+γ}$ regularity result for solutions at their singular free boundary points. We also show a corresponding non-degeneracy estimate.

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Jimmy Lamboley, Yannick Sire, Eduardo V. Teixeira. 2020-01-07. Free boundary problems involving singular weights. https://arxiv.org/abs/1711.08339

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