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


 
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1. Title Title of document Uniqueness for Fokker-Planck equations with measurable coefficients and applications to the fast diffusion equation
 
2. Creator Author's name, affiliation, country Nadia Belaribi; Université Paris 13 and ENSTA ParisTech; France
 
2. Creator Author's name, affiliation, country Francesco Russo; ENSTA ParisTech; France
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Fokker-Planck; fast diffusion; probabilistic representation;non-linear diffusion; stochastic particle algorithm.
 
3. Subject Subject classification 60H30; 60G44; 60J60; 60H07; 35C99; 35K10; 35K55; 35K65; 65C05; 65C35
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) ANR Project MASTERIE 2010 BLAN 0121 01
 
7. Date (YYYY-MM-DD) 2012-10-02
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2349
 
10. Identifier Digital Object Identifier 10.1214/EJP.v17-2349
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 17
 
12. Language English=en en
 
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