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.

In this paper we study the Fokker-Planck operator with potential $V\left(x\right)$, 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.

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Classification : 35H10,  47A10
@article{ASNSP_2012_5_11_4_789_0,
author = {Li, Wei-Xi},
title = {Global hypoellipticity and compactness of resolvent for Fokker-Planck operator},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {789--815},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 11},
number = {4},
year = {2012},
zbl = {1261.35046},
mrnumber = {3060700},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2012_5_11_4_789_0/}
}
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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