Uniqueness for Fokker-Planck equations with measurable coefficients and applications to the fast diffusion equation
نویسندگان
چکیده
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 ∂tu = ∂ 2 xxu m with m ∈]0, 1[. Together with the mentioned Fokker-Planck equation, we make use of small time density estimates uniformly with respect to the initial condition.
منابع مشابه
About Fokker-Planck equation with measurable coefficients: application to the fast diffusion equation
Abstract. 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 ∂tu = ∂ 2 xx u with m ∈ (0, 1)...
متن کاملExistence and uniqueness of solutions to Fokker-Planck type equations with irregular coefficients
We study the existence and the uniqueness of the solution to a class of Fokker-Planck type equations with irregular coefficients, more precisely with coefficients in Sobolev spaces W . Our arguments are based upon the DiPerna-Lions theory of renormalized solutions to linear transport equations and related equations [6]. The present work extends the results of our previous article [17], where on...
متن کاملUniqueness of degenerate Fokker – Planck equations with weakly differentiable drift whose gradient is given by a singular integral ∗
In this paper we prove the uniqueness of solutions to degenerate Fokker–Planck equations with bounded coefficients, under the additional assumptions that the diffusion coefficient has W 1,2 loc regularity, while the gradient of the drift coefficient is merely given by a singular integral.
متن کاملDegenerate irregular SDEs with jumps and application to integro-differential equations of Fokker-Planck type
We investigate stochastic differential equations with jumps and irregular coefficients, and obtain the existence and uniqueness of generalized stochastic flows. Moreover, we also prove the existence and uniqueness of L-solutions or measure-valued solutions for second order integro-differential equation of Fokker-Planck type.
متن کاملSteady States of Fokker-planck Equations: I. Existence
This is the first paper in a series concerning the study of steady states of a Fokker-Planck equation in a general domain in R with Lp̄loc drift term and W 1,p̄ loc diffusion term for any p̄ > n. In this paper, by using the level set method especially the integral identity which we introduced in [24], we obtain several new existence results of steady states, including stationary solutions and meas...
متن کامل