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Regularity for almost-minimizers of variable coefficient Bernoulli-type functionals

Regularity for almost-minimizers of variable coefficient Bernoulli-type functionals In David et al. (Adv Math 350:1109–1192, 2019) and David and Toro (Regularity of almost minimizers with free boundary. Calculus of variations and PDEs, 2020), the authors studied almost minimizers for functionals of the type first studied by Alt and Caffarelli (J Reine Angew Math 325:105–144, 1981) and Alt et al. (Trans Am Math Soc 282:431–461, 1984). In this paper we study the regularity of almost minimizers to energy functionals with variable coefficients (as opposed to Alt and Caffarelli, J Reine Angew Math 325:105–144, 1981; Alt et al., Trans Am Math Soc 282:431–461, 1984; David et al., Adv Math 350:1109–1192, 2019; David and Toro, Regularity of almost minimizers with free boundary. Calculus of variations and PDEs, 2020) which deal only with the “Laplacian” setting). We prove Lipschitz regularity up to, and across, the free boundary, fully generalizing the results of David and Toro (Regularity of almost minimizers with free boundary. Calculus of variations and PDEs, 2020) to the variable coefficient setting. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

Regularity for almost-minimizers of variable coefficient Bernoulli-type functionals

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Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021
ISSN
0025-5874
eISSN
1432-1823
DOI
10.1007/s00209-021-02719-5
Publisher site
See Article on Publisher Site

Abstract

In David et al. (Adv Math 350:1109–1192, 2019) and David and Toro (Regularity of almost minimizers with free boundary. Calculus of variations and PDEs, 2020), the authors studied almost minimizers for functionals of the type first studied by Alt and Caffarelli (J Reine Angew Math 325:105–144, 1981) and Alt et al. (Trans Am Math Soc 282:431–461, 1984). In this paper we study the regularity of almost minimizers to energy functionals with variable coefficients (as opposed to Alt and Caffarelli, J Reine Angew Math 325:105–144, 1981; Alt et al., Trans Am Math Soc 282:431–461, 1984; David et al., Adv Math 350:1109–1192, 2019; David and Toro, Regularity of almost minimizers with free boundary. Calculus of variations and PDEs, 2020) which deal only with the “Laplacian” setting). We prove Lipschitz regularity up to, and across, the free boundary, fully generalizing the results of David and Toro (Regularity of almost minimizers with free boundary. Calculus of variations and PDEs, 2020) to the variable coefficient setting.

Journal

Mathematische ZeitschriftSpringer Journals

Published: May 5, 2021

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