Catenoidal Layers for the Allen-Cahn Equation in Bounded Dom

发布时间：2018-11-07 14:01

【摘要】：This paper presents a new family of solutions to the singularly perturbed Allen-Cahn equation α~2Δu + u(1- u~2) = 0 in a smooth bounded domain Ω 銰R~3, 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.
[Abstract]:This paper presents a new family of solutions to the singularly perturbed Allen-Cahn equation 伪 ~ 2 螖 u u (1- U ~ 2) = 0 in a smooth bounded domain 惟 This paper presents a new family of solutions to the singularly perturbed Allen-Cahn equation 3, with Neumann boundary condition and 伪 0 a small parameter. These solutions have the property that as 伪 O, their level sets collapse onto a bounded portion of a complete embedded minimal surface with finite total curvature intersecting? 惟 orthogonally and that is non-degenerate respect to? 惟. The authors provide explicit examples of surfaces to which the result applies.
【作者单位】： Department
【基金】：supported by the Grant 13-00863S of the Grant Agency of the Czech Republic grants Fondecyt 1150066,Fondo Basal CMM,Millenium Nucleus CAPDE NC130017 NSERC accelerator
【分类号】：O175.8

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