Free boundary problems involving singular weights

Published 22 Nov 2017 in math.AP | (1711.08339v4)

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 $C^{1+\gamma}$ regularity result for solutions at their singular free boundary points. We also show a corresponding non-degeneracy estimate.

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