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Archive for Rational Mechanics and Analysis

, Volume 171, Issue 2, pp 151–218 | Cite as

Isotropic Hypoellipticity and Trend to Equilibrium for the Fokker-Planck Equation with a High-Degree Potential

  • Frédéric Hérau
  • Francis NierEmail author
Article

Abstract.

We consider the Fokker-Planck equation with a confining or anti-confining potential which behaves at infinity like a possibly high-degree homogeneous function. Hypoellipticity techniques provide the well-posedness of the weak Cauchy problem in both cases as well as instantaneous smoothing and exponential trend to equilibrium. Lower and upper bounds for the rate of convergence to equilibrium are obtained in terms of the lowest positive eigenvalue of the corresponding Witten Laplacian, with detailed applications.

Keywords

Cauchy Problem Positive Eigenvalue Homogeneous Function Exponential Trend Detailed Application 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques UFR Sciences exactes et naturellesUniversité de ReimsReims cedex 9FRANCE
  2. 2.IRMAR, UMR-CNRS 6625 Campus de beaulieuUniversité de RennesFRANCE

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