On the Stationary Cahn-Hilliard Equation: Bubble Solutions

We study stationary solutions of the Cahn--Hilliard equation in a bounded smooth domain which have an interior spherical interface (bubbles). We show that a large class of interior points (the ``nondegenerate peak'' points) have the following property: there exists such a solution whose bubble center lies close to a given nondegenerate peak point. Our construction uses among others the Liapunov-Schmidt reduction method and exponential asymptotics