Global Hypoellipticity and Compactness of Resolvent for Fokker-Planck Operator
(2010)- Abstract
- 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 H´erau-Nier and Helffer-Nier, by obtaining a better global hypoelliptic estimate under weaker assumptions on the potential.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1749021
- author
- Li, Wei-Xi LU
- organization
- publishing date
- 2010
- type
- Other contribution
- publication status
- published
- subject
- keywords
- global hypoellipticity, compact resolvent, Fokker-Planc k operator, Witten Laplace operator
- pages
- 23 pages
- language
- English
- LU publication?
- yes
- id
- 8ca09610-59ca-48fc-a8a0-ac5f2cdfbaa4 (old id 1749021)
- alternative location
- http://arxiv.org/abs/0910.1049
- date added to LUP
- 2016-04-04 11:54:39
- date last changed
- 2020-12-03 13:35:11
@misc{8ca09610-59ca-48fc-a8a0-ac5f2cdfbaa4, abstract = {{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).<br/><br> 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 H´erau-Nier and Helffer-Nier, by obtaining a better global hypoelliptic estimate under weaker assumptions on the potential.}}, author = {{Li, Wei-Xi}}, keywords = {{global hypoellipticity; compact resolvent; Fokker-Planc k operator; Witten Laplace operator}}, language = {{eng}}, title = {{Global Hypoellipticity and Compactness of Resolvent for Fokker-Planck Operator}}, url = {{http://arxiv.org/abs/0910.1049}}, year = {{2010}}, }