Global Hypoellipticity and Compact Resolvent for Fokker-Planck Operator
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Wei-Xi Li [1]
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[1] Wuhan University
Wuhan University
China
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- Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 11, Nº 4, 2012, págs. 789-815
- Idioma: inglés
- Enlaces
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Resumen
Inthis paper westudytheFokker-Planckoperator withpotential 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 [5] and Helffer-Nier [3], by obtaining a better global hypoelliptic estimate under weaker assumptions on the potential.
