Hypoelliptic estimates for some linear diffusive kinetic equations

Frédéric Hérau[1]

  • [1] Laboratoire de Mathématiques Jean Leray 2, rue de la Houssinière - BP 92208 F-44322 Nantes Cedex 3

Journées Équations aux dérivées partielles (2010)

  • page 1-13
  • ISSN: 0752-0360

Abstract

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This note is an announcement of a forthcoming paper [13] in collaboration with K. Pravda-Starov on global hypoelliptic estimates for Fokker-Planck and linear Landau-type operators. Linear Landau-type equations are a class of inhomogeneous kinetic equations with anisotropic diffusion whose study is motivated by the linearization of the Landau equation near the Maxwellian distribution. By introducing a microlocal method by multiplier which can be adapted to various hypoelliptic kinetic equations, we establish optimal global hypoelliptic estimates with loss of 4 / 3 derivatives in a Sobolev scale exactly related to the anisotropy of the diffusion.

How to cite

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Hérau, Frédéric. "Hypoelliptic estimates for some linear diffusive kinetic equations." Journées Équations aux dérivées partielles (2010): 1-13. <http://eudml.org/doc/116390>.

@article{Hérau2010,
abstract = {This note is an announcement of a forthcoming paper [13] in collaboration with K. Pravda-Starov on global hypoelliptic estimates for Fokker-Planck and linear Landau-type operators. Linear Landau-type equations are a class of inhomogeneous kinetic equations with anisotropic diffusion whose study is motivated by the linearization of the Landau equation near the Maxwellian distribution. By introducing a microlocal method by multiplier which can be adapted to various hypoelliptic kinetic equations, we establish optimal global hypoelliptic estimates with loss of $4/3$ derivatives in a Sobolev scale exactly related to the anisotropy of the diffusion.},
affiliation = {Laboratoire de Mathématiques Jean Leray 2, rue de la Houssinière - BP 92208 F-44322 Nantes Cedex 3},
author = {Hérau, Frédéric},
journal = {Journées Équations aux dérivées partielles},
keywords = {Kinetic equations; Regularity; global hypoelliptic estimates; hypoellipticity; anisotropic diffusion; Wick quantization; Landau; Fokker-Planck},
language = {eng},
month = {6},
pages = {1-13},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Hypoelliptic estimates for some linear diffusive kinetic equations},
url = {http://eudml.org/doc/116390},
year = {2010},
}

TY - JOUR
AU - Hérau, Frédéric
TI - Hypoelliptic estimates for some linear diffusive kinetic equations
JO - Journées Équations aux dérivées partielles
DA - 2010/6//
PB - Groupement de recherche 2434 du CNRS
SP - 1
EP - 13
AB - This note is an announcement of a forthcoming paper [13] in collaboration with K. Pravda-Starov on global hypoelliptic estimates for Fokker-Planck and linear Landau-type operators. Linear Landau-type equations are a class of inhomogeneous kinetic equations with anisotropic diffusion whose study is motivated by the linearization of the Landau equation near the Maxwellian distribution. By introducing a microlocal method by multiplier which can be adapted to various hypoelliptic kinetic equations, we establish optimal global hypoelliptic estimates with loss of $4/3$ derivatives in a Sobolev scale exactly related to the anisotropy of the diffusion.
LA - eng
KW - Kinetic equations; Regularity; global hypoelliptic estimates; hypoellipticity; anisotropic diffusion; Wick quantization; Landau; Fokker-Planck
UR - http://eudml.org/doc/116390
ER -

References

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