A vectorial problem with thin free boundary

被引：2

作者：

De Silva, Daniela ^{[1
]}

Tortone, Giorgio ^{[2
]}

机构：

[1] Columbia Univ, Barnard Coll, Dept Math, New York, NY 10027 USA

[2] Univ Pisa, Dipartimento Matemat, Largo Bruno Pontecorvo 5, I-56127 Pisa, Italy

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2023年 / 62卷 / 08期

基金：

欧洲研究理事会;

关键词：

REGULARITY;

D O I：

10.1007/s00526-023-02561-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the vectorial analogue of the thin free boundary problem introduced by Caffarelli et al. (JEur math Soc 12:1151-1179, 2010) as a realization of a nonlocal version of the classical Bernoulli problem. We study optimal regularity, nondegeneracy, and density properties of local minimizers. Via a blow-up analysis based on a Weiss type monotonicity formula, we show that the free boundary is the union of a "regular" and a "singular" part. Finally we use a viscosity approach to prove C-1,C-alpha regularity of the regular part of the free boundary.

引用

页数：34

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