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Global Hypoellipticity and Compactness of Resolvent for Fokker-Planck Operator

Li, Wei-Xi LU (2010) In ARXIV
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:
author
organization
publishing date
type
Contribution to journal
publication status
unpublished
subject
keywords
global hypoellipticity, compact resolvent, Fokker-Planc k operator, Witten Laplace operator
in
ARXIV
pages
23 pages
publisher
Cornell University Library
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
2013-12-12 14:29:18
date last changed
2016-04-16 09:52:14
@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},
  keyword      = {global hypoellipticity,compact resolvent,Fokker-Planc k operator,Witten Laplace operator},
  language     = {eng},
  pages        = {23},
  publisher    = {ARRAY(0xb6caea8)},
  series       = {ARXIV},
  title        = {Global Hypoellipticity and Compactness of Resolvent for Fokker-Planck Operator},
  year         = {2010},
}