On critical points of the relative fractional perimeter

IF 1.8 1区数学 Q1 MATHEMATICS, APPLIED

Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2021-09-01 DOI:10.1016/j.anihpc.2020.11.005

Andrea Malchiodi , Matteo Novaga , Dayana Pagliardini

引用次数: 1

Abstract

We study the localization of sets with constant nonlocal mean curvature and prescribed small volume in a bounded open set, proving that they are sufficiently close to critical points of a suitable nonlocal potential. We then consider the fractional perimeter in half-spaces. We prove existence of minimizers under fixed volume constraint, and we show some properties such as smoothness and rotational symmetry.

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关于相对分数周长的临界点

我们研究了具有常非局部平均曲率和规定小体积的集在有界开集中的局部化，证明了它们足够接近合适的非局部势的临界点。然后我们考虑半空间中的分数周长。我们证明了在固定体积约束下极小值的存在性，并给出了一些性质，如光滑性和旋转对称性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annales De L Institut Henri Poincare-Analyse Non Lineaire 数学-应用数学

CiteScore

4.10

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Nonlinear Analysis section of the Annales de l''Institut Henri Poincaré is an international journal created in 1983 which publishes original and high quality research articles. It concentrates on all domains concerned with nonlinear analysis, specially applicable to PDE, mechanics, physics, economy, without overlooking the numerical aspects.