Articulo
Catenoidal Layers for the Allen-Cahn Equation in Bounded Domains
Chinese Annals of Mathematics, Series B
Registro en:
1150066
1150066
Autor
Agudelo, Oscar
Del Pino-Manresa, Manuel Adrián
Wei, Juncheng
Institución
Resumen
This paper presents a new family of solutions to the singularly perturbed Allen-Cahn equation alpha(2)Delta u + u(1 - u(2)) = 0 in a smooth bounded domain Omega subset of R-3, with Neumann boundary condition and alpha > 0 a small parameter. These solutions have the property that as alpha -> 0, their level sets collapse onto a bounded portion of a complete embedded minimal surface with finite total curvature intersecting partial derivative Omega orthogonally and that is non-degenerate respect to partial derivative Omega. The authors provide explicit examples of surfaces to which the result applies. Keywords, Author Keywords:Allen-Cahn equation Critical minimal surfaces Critical catenoid Infinite dimensional gluing method Neumann boundary condition Regular 2015 FONDECYT FONDECYT