Global Hypoellipticity and Compactness of Resolvent for Fokker-Planck Operator
Analysis of PDEs
2010-09-14 v3 Spectral Theory
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. 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.
Cite
@article{arxiv.0910.1049,
title = {Global Hypoellipticity and Compactness of Resolvent for Fokker-Planck Operator},
author = {Wei-Xi Li},
journal= {arXiv preprint arXiv:0910.1049},
year = {2010}
}
Comments
Lemma 4.6 is corrected