Catenoidal layers for the Allen-Cahn equation in bounded domains

被引：0
|
作者：
Oscar Agudelo
Manuel Del Pino
Juncheng Wei
机构：
[1] Západočescká Univerzita v Plzni,Department of Mathematics
[2] Universidad de Chile,Departamento de Ingeniería Matemática and CMM
[3] University of British Columbia,Department of Mathematics
来源：
Chinese Annals of Mathematics, Series B | 2017年 / 38卷
关键词：
Allen-Cahn equation; Critical minimal surfaces; Critical catenoid; Infinite dimensional gluing method; Neumann boundary condition; 35J60; 35B25; 58J35;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper presents a new family of solutions to the singularly perturbed Allen-Cahn equation α2Δu + u(1 − u2) = 0 in a smooth bounded domain Ω ⊂ R3, with Neumann boundary condition and α > 0 a small parameter. These solutions have the property that as α → 0, their level sets collapse onto a bounded portion of a complete embedded minimal surface with finite total curvature intersecting ∂Ω orthogonally and that is non-degenerate respect to ∂Ω. The authors provide explicit examples of surfaces to which the result applies.
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页码：13 / 44
页数：31
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