On the classification of solutions to an elliptic equation involving the Grushin operator
Cung The Anh, Ji Hoon Lee, Bui Kim My · Complex Variables and Elliptic Equations · 2017
We prove that, for , the degenerate elliptic equation involving the Grushin operator on the whole space does not admit any solution stable outside a compact set of . The result is sharp and obtained without any assumption about the boundedness of solutions. In particular, when , we recover the previous results for the Laplace operator in [Farina, C R Math Acad Sci Paris. 2007;345:63–66] and [Dancer and Farina, Proc Am Math Soc.2009;137:1333–1338].