Electronic Journal of Probability

Uniqueness for Fokker-Planck equations 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 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.

Article information

Source
Electron. J. Probab. Volume 17 (2012), paper no. 84, 28 pp.

Dates
Accepted: 2 October 2012
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465062406

Digital Object Identifier
doi:10.1214/EJP.v17-2349

Mathematical Reviews number (MathSciNet)
MR2988399

Zentralblatt MATH identifier
1268.82024

Rights

Citation

Belaribi, Nadia; Russo, Francesco. Uniqueness for Fokker-Planck equations with measurable coefficients and applications to the fast diffusion equation. Electron. J. Probab. 17 (2012), paper no. 84, 28 pp. doi:10.1214/EJP.v17-2349. https://projecteuclid.org/euclid.ejp/1465062406

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