A symmetry result for the ornstein-uhlenbeck operator

Annalisa Cesaroni, Matteo Novaga, Enrico Valdinoci

Research output: Contribution to journalArticlepeer-review

11 Citations (Web of Science)


In 1978 E. De Giorgi formulated a conjecture concerning the onedimensional symmetry of bounded solutions to the elliptic equation u = F0(u), which are monotone in some direction. In this paper we prove the analogous statement for the equation uδ hx;ruiu = F0(u), where the Laplacian is replaced by the Ornstein-Uhlenbeck operator. Our theorem holds without any restriction on the dimension of the ambient space, and this allows us to obtain an similar result in innite dimensions by a limit procedure.

Original languageEnglish
Pages (from-to)2451-2467
Number of pages17
JournalDiscrete and Continuous Dynamical Systems- Series A
Issue number6
Publication statusPublished - 1 Jun 2014
Externally publishedYes


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