|
|
| |
| Catenoidal Layers for the Allen-Cahn Equation in Bounded Domains |
| |
Citation： |
Oscar AGUDELO,Manuel DEL PINO,Juncheng WEI.Catenoidal Layers for the Allen-Cahn Equation in Bounded Domains[J].Chinese Annals of Mathematics B,2017,38(1):13~44 |
| Page view： 791
Net amount： 637 |
Authors： |
Oscar AGUDELO; Manuel DEL PINO;Juncheng WEI |
Foundation： |
This work was supported by the Grant 13-00863S of the Grant
Agency of the Czech Republic, grants Fondecyt 1150066, Fondo Basal
CMM, Millenium. Nucleus CAPDE NC130017 and NSERC accelerator. |
|
|
| Abstract： |
This paper presents a new family of solutions to the singularly
perturbed Allen-Cahn equation $\A^2 \Delta u + u(1-u^2)=0$ in a
smooth bounded domain $\Omega\subset \R^3$, with Neumann boundary
condition and $\A>0$ a small parameter. These solutions have the
property that as $\A\to0$, their level sets collapse onto a bounded
portion of a complete embedded minimal surface with finite total
curvature intersecting $\pp \Omega$ orthogonally and that is
non-degenerate respect to $\pp \Omega$. The authors provide explicit
examples of surfaces to which the result applies. |
Keywords： |
Allen-Cahn equation, Critical minimal surfaces, Critical catenoid,Infinite dimensional gluing method, Neumann boundary condition |
Classification： |
35J60, 35B25, 58J35 |
|
|
Download PDF Full-Text
|
|
|
|
