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Pré-Publication, Document De Travail Année : 2009

Global Hypoellipticity and Compactness of Resolvent for Fokker-Planck Operator

Wei-Xi Li
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Résumé

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.

Dates et versions

hal-00422436 , version 1 (07-10-2009)

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Citer

Wei-Xi Li. Global Hypoellipticity and Compactness of Resolvent for Fokker-Planck Operator. 2009. ⟨hal-00422436⟩
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