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Free boundary problems involving singular weights

Lamboley, Jimmy; Sire, Yannick; Teixeira, Eduardo (2020), Free boundary problems involving singular weights, Communications in Partial Differential Equations, 45, 7, p. 758-775. 10.1080/03605302.2020.1716003

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Type
Article accepté pour publication ou publié
Date
2020
Journal name
Communications in Partial Differential Equations
Volume
45
Number
7
Publisher
Taylor & Francis
Pages
758-775
Publication identifier
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Author(s)
Lamboley, Jimmy
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Sire, Yannick
Institut de Mathématiques de Marseille [I2M]
Teixeira, Eduardo
Department of Mathematics [University of Central Florida]
Abstract (EN)
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.
Subjects / Keywords
Free boundary problems; Muckenhoupt weights; geometricregularity