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arXiv · 0910.1049

Global Hypoellipticity and Compactness of Resolvent for Fokker-Planck Operator

Wei-Xi Li
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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 Hérau-Nier and Helffer-Nier, by obtaining a better global hypoelliptic estimate under weaker assumptions on the potential.

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Wei-Xi Li. 2010-09-11. Global Hypoellipticity and Compactness of Resolvent for Fokker-Planck Operator. https://arxiv.org/abs/0910.1049

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