UNIFORM STABILITY IN THE EUCLIDEAN ISOPERIMETRIC PROBLEM FOR THE ALLEN-CAHN ENERGY

被引：1

作者：

Maggi, Francesco ^{[1
]}

Restrepo, Daniel ^{[1
]}

机构：

[1] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

来源：

ANALYSIS & PDE | 2024年 / 17卷 / 05期

关键词：

isoperimetric problem; Allen-Cahn energy; Alexandrov theorem; GRADIENT THEORY; SOBOLEV INEQUALITY; PHASE-TRANSITIONS; CONVERGENCE; INTERFACES; EQUATIONS; VAN;

D O I：

10.2140/apde.2024.17.1761

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the isoperimetric problem defined on the whole R n by the Allen-Cahn energy functional. For nondegenerate double -well potentials, we prove sharp quantitative stability inequalities of quadratic type which are uniform in the length scale of the phase transitions. We also derive a rigidity theorem for critical points analogous to the classical Alexandrov theorem for constant mean curvature boundaries.

引用

页码：1761 / 1830

页数：73

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