Catenoidal layers for the Allen-Cahn equation in bounded domains

O. Agudelo, Manuel del Pino, Juncheng Wei

In this paper we present a new family of solutions to the singularly perturbed Allen-Cahn equation ${\alpha }^2\Delta u+u(1-u^2)=0,in\; \Omega \subset {\mathbb{R}}^N$ where $N=3$, $\Omega$ is a smoot…