Geodesic
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

Voir la notice de l'article provenant de la source Numdam

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 
@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},
     mrnumber = {3060700},
     zbl = {1261.35046},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2012_5_11_4_789_0/}
}
TY  - JOUR
AU  - Li, Wei-Xi
TI  - Global hypoellipticity and compactness of resolvent for Fokker-Planck operator
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 2012
SP  - 789
EP  - 815
VL  - 11
IS  - 4
PB  - Scuola Normale Superiore, Pisa
UR  - http://geodesic.mathdoc.fr/item/ASNSP_2012_5_11_4_789_0/
LA  - en
ID  - ASNSP_2012_5_11_4_789_0
ER  - 
%0 Journal Article
%A Li, Wei-Xi
%T Global hypoellipticity and compactness of resolvent for Fokker-Planck operator
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 2012
%P 789-815
%V 11
%N 4
%I Scuola Normale Superiore, Pisa
%U http://geodesic.mathdoc.fr/item/ASNSP_2012_5_11_4_789_0/
%G en
%F 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://geodesic.mathdoc.fr/item/ASNSP_2012_5_11_4_789_0/