I will talk about some recent results obtained in collaboration with E. Valdinoci and V. O. Savin. We consider weak solutions of div(−Du(x)−p−2Du(x))=h0’(u(x)) where h0 is a double-well potential. We prove that level sets of local minimizers of the energy functional are hyperplanes if N<8. This provides the proof of a result which is the generalization to the case p>1 of a conjecture of De Giorgi, recently solved by V.O. Savin for the case p=2.