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Journal Articles Electronic Journal of Probability Year : 2012

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

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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Dates and versions

hal-00645483 , version 1 (28-11-2011)
hal-00645483 , version 2 (17-09-2012)

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Nadia Belaribi, Francesco Russo. About Fokker-Planck equation with measurable coefficients and applications to the fast diffusion equation. Electronic Journal of Probability, 2012, 17 (84), pp.1-28. ⟨hal-00645483v2⟩
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