# About Fokker-Planck equation with measurable coefficients and applications to the fast diffusion equation

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3 MATHFI - Financial mathematics
Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech, UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12
Abstract : 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
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https://hal.inria.fr/hal-00645483
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Submitted on : Monday, September 17, 2012 - 7:56:42 PM
Last modification on : Wednesday, April 28, 2021 - 6:46:22 PM
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### Identifiers

• HAL Id : hal-00645483, version 2
• ARXIV : 1111.6458

### Citation

Nadia Belaribi, Francesco Russo. About Fokker-Planck equation with measurable coefficients and applications to the fast diffusion equation. 2012. ⟨hal-00645483v2⟩

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