On the stationary Cahn-Hilliard equation: Interior spike solutions

Abstract

We study solutions of the stationary Cahn-Hilliard equation in a bounded smooth domain which have a spike in the interior. We show that a large class of interior points (the "nondegenerate peak" points) have the following property: There exist such solutions whose spike lies close to a given nondegenerate peak point. Our construction uses among others the methods of viscosity solution, weak convergence of measures, and Liapunov-Schmidt reduction. © 1998 Academic Press.