Regularity for almost-minimizers of variable coefficient Bernoulli-type functionals
Regularity for almost-minimizers of variable coefficient Bernoulli-type functionals
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DOI：
10.1007/s00209-021-02719-5
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发表时间：
2021-05-05
影响因子：
0.8
通讯作者：
Toro, Tatiana
中科院分区：
文献类型：
--
作者：
David, Guy;Engelstein, Max;Toro, Tatiana
在大卫等人（Adv Math 350：1109-1192，2019）和大卫和托罗（几乎极小化与自由边界的正则性。变分法和偏微分方程，2020），作者研究了几乎极小化的泛函的类型首先研究的Alt和Caffarelli（J Reine Angew Math 325：105-144，1981）和Alt等人（Trans Am Math Soc 282：431-461，1984）。在本文中，我们研究了具有可变系数的能量泛函的几乎最小化器的正则性（与Alt和Caffarelli，J Reine Angew Math 325：105-144，1981; Alt等人，Trans Am Math Soc 282：431-461，1984;大卫等人，Adv Math 350：1109-1192，2019;大卫和托罗，几乎极小化的正则性与自由边界。变分法和偏微分方程，2020年），只处理“拉普拉斯”设置）。我们证明了Lipschitz正则性直到自由边界和穿过自由边界，完全推广了大卫和Toro（Regularity of almost minimizers with free boundary.变分法和偏微分方程，2020）的可变系数设置。
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.