Periodic solutions to the Cahn-Hilliard equation in the plane

Andrea Malchiodi, Rainer Mandel, Matteo Rizzi

In this paper we construct entire solutions to the Cahn-Hilliard equation $-\Delta (-\Delta u+W^{{}^{\prime }}(u))+W^{"}(u)(-\Delta u+W^{{}^{\prime }}(u))=0$ in the Euclidean plane, where $W(u)$ is the standard double-we…