Global hypoellipticity and compactness of resolvent for Fokker-Planck operator
Li, Wei-Xi1
1 School of Mathematics and Statistics Wuhan University 430072 Wuhan, China
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 11 (2012) no. 4, pp. 789-815.

In this paper we study the Fokker-Planck operator with potential V(x), and analyze some kind of conditions imposed on the potential to ensure the validity of global hypoelliptic estimates (see Theorem 1.1). As a consequence, we obtain the compactness of resolvent of the Fokker-Planck operator if either the Witten Laplacian on 0-forms has a compact resolvent or some additional assumption on the behavior of the potential at infinity is fulfilled. This work improves the previous results of Hérau-Nier [5] and Helffer-Nier [3], by obtaining a better global hypoelliptic estimate under weaker assumptions on the potential.

Publié le :
Classification : 35H10, 47A10
Li, Wei-Xi 1

1 School of Mathematics and Statistics Wuhan University 430072 Wuhan, China 
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Li, Wei-Xi. Global hypoellipticity and compactness of resolvent for Fokker-Planck operator. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 11 (2012) no. 4, pp. 789-815. http://www.numdam.org/item/ASNSP_2012_5_11_4_789_0/

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