Free boundary problems involving singular weights. Issue 7 (2nd July 2020) - Lamboley, Jimmy; Sire, Yannick; Teixeira, Eduardo V.
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, boundedness, and continuity 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 nondegeneracy estimate.