Isabeau Birindelli, Enrico Valdinoci
On the Allen-Cahn
equation in the Grushin plane:
a monotone entire solution
that is not one-dimensional
(42K, LaTeX)

ABSTRACT.  We consider solutions of the Allen-Cahn equation in the whole Grushin 
plane and we show that if they are monotone in the vertical direction, 
then they are stable and they satisfy a good energy estimate.
However, they are not necessarily
one-dimensional, as a counter-example shows.