Stable solutions of the Allen-Cahn equation in dimension 8 and minimal   cones
  In this paper, we are interested in bounded, entire, solutions of the Allen-Cahn equation which are defined in Euclidean space and whose zero set is asymptotic to a given minimal cone. In particular, in dimension larger than or equal to 8, we prove the existence of stable solutions of the Allen-Cahn equation whose zero sets are not hyperplanes. 
Frank Pacard and Juncheng Wei
math.AP