Isotropic hypoellipticity and trend to the equilibrium for the Fokker-Planck equation with high degree potential

Frédéric Hérau

Journées équations aux dérivées partielles (2002)

  • page 1-13
  • ISSN: 0752-0360

Abstract

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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

How to cite

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Hérau, Frédéric. "Isotropic hypoellipticity and trend to the equilibrium for the Fokker-Planck equation with high degree potential." Journées équations aux dérivées partielles (2002): 1-13. <http://eudml.org/doc/93435>.

@article{Hérau2002,
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},
author = {Hérau, Frédéric},
journal = {Journées équations aux dérivées partielles},
language = {eng},
pages = {1-13},
publisher = {Université de Nantes},
title = {Isotropic hypoellipticity and trend to the equilibrium for the Fokker-Planck equation with high degree potential},
url = {http://eudml.org/doc/93435},
year = {2002},
}

TY - JOUR
AU - Hérau, Frédéric
TI - Isotropic hypoellipticity and trend to the equilibrium for the Fokker-Planck equation with high degree potential
JO - Journées équations aux dérivées partielles
PY - 2002
PB - Université de Nantes
SP - 1
EP - 13
AB - 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
LA - eng
UR - http://eudml.org/doc/93435
ER -

References

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