Artículo de revista
Catenoidal layers for the Allen-Cahn equation in bounded domains
Fecha
2017Registro en:
Chinese Annals of Mathematics. Series B, Volumen 38, Issue 1, 2017, Pages 13-44
18606261
02529599
10.1007/s11401-016-1062-5
Autor
Agudelo, Oscar
Pino Manresa, Manuel del
Wei, Juncheng
Institución
Resumen
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.