Some rigidity results and asymptotic properties for solutions to semilinear elliptic P.D.E.

Abstract

We will present some rigidity results for solutions to semilinear elliptic equations of the form Delta u= W'(u), where W is a quite general potential with a local minimum and a local maximum. We are particularly interested in Liouville-type theorems and symmetry results, which generalise some known facts about the Cahn-Hilliard equation.