Radial and cylindrical symmetry of solutions to the Cahn-Hilliard equation

Abstract

The paper is devoted to the classification of entire solutions to the Cahn-Hilliard equation $-\Delta u=u-u^3-\delta$ in ${\mathbb{R}}^N$, with particular interest in those solutions whose nodal set is either bounded or contained in a cylinder. The aim is to prove either radial or cylindrical symmetry, under suitable hypothesis.