Uniqueness for Fokker-Planck equations with measurable coefficients and applications to the fast diffusion equation

Nadia Belaribi (Université Paris 13 and ENSTA ParisTech)
Francesco Russo (ENSTA ParisTech)


The object of this paper is the uniqueness for a $d$-dimensional Fokker-Planck type equation with inhomogeneous (possibly degenerated) measurable not necessarily bounded coefficients. We provide an application to the probabilistic representation of  the so-called Barenblatt's 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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Pages: 1-28

Publication Date: October 2, 2012

DOI: 10.1214/EJP.v17-2349


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