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

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

2011-11-28

arxiv.org/abs/1111.6458v1

Mathematics

Probability

Scientific paper

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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