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

   
@article{EJP2349,
	author = {Nadia Belaribi and Francesco Russo},
	title = {Uniqueness for Fokker-Planck equations with measurable coefficients and applications to the fast diffusion equation},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {17},
	year = {2012},
	keywords = {Fokker-Planck; fast diffusion; probabilistic representation;non-linear diffusion; stochastic particle algorithm.},
	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.},
	pages = {no. 84, 1-28},
	issn = {1083-6489},
	doi = {10.1214/EJP.v17-2349},    
        url = {http://ejp.ejpecp.org/article/view/2349}}