HAL - INRIA :: [hal-00645483, version 1] About Fokker-Planck equation with measurable coefficients: application to the fast diffusion equation

hal-00645483, version 1

About Fokker-Planck equation with measurable coefficients: application to the fast diffusion equation

Nadia Belaribi () ^1, 2, Francesco Russo ( Auteur à contacter de préférence , )^a^, 1, 3

Résumé : The object of this paper is the uniqueness for a $d$-dimensional Fokker-Planck type equation with non-homogeneous (possibly degenerated) measurable not necessarily bounded coefficients. We provide an application to the probabilistic representation of the so called Barenblatt solution of the fast diffusion equation which is the partial differential equation $\partial_t u = \partial^2_{xx} u^m$ with $m\in(0,1)$. Together with the mentioned Fokker-Planck equation, we make use of small time density estimates uniformly with respect to the initial condition

a – ENSTA ParisTech
1 : Unité de Mathématiques Appliquées (UMA)
ENSTA ParisTech
2 : Laboratoire d'Analyse, Géométrie et Applications (LAGA)
CNRS : UMR7539 – Université Paris XIII - Paris Nord – Université Paris VIII - Vincennes Saint-Denis
3 : MATHFI (INRIA Rocquencourt)
INRIA – Ecole des Ponts ParisTech – Université Paris XII - Paris Est Créteil Val-de-Marne

hal-00645483, version 1
http://hal.inria.fr/hal-00645483
oai:hal.inria.fr:hal-00645483
Contributeur : Francesco Russo <>
Soumis le : Lundi 28 Novembre 2011, 10:49:21
Dernière modification le : Lundi 28 Novembre 2011, 15:52:26

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arXiv : 1111.6458

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