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

摘要

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 $min]0,1[$.?Together with the mentioned Fokker-Planck equation,?we make use of small time density estimates uniformly with respect to the initial condition.