Global Hypoellipticity and Compactness of Resolvent for Fokker-Planck Operator

Details Global Hypoellipticity and Compactness of Resolvent for Fokker-Planck Operator Global Hypoellipticity and Compactness of Resolvent for Fokker-Planck Operator

2009-10-06

arxiv.org/abs/0910.1049v3

Mathematics

Analysis of PDEs

Lemma 4.6 is corrected

Scientific paper

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.

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