Uniqueness for nonlinear Fokker–Planck equations and weak uniqueness for McKean–Vlasov SDEs

被引：0

作者：

Viorel Barbu

Michael Röckner

机构：

[1] Octav Mayer Institute of Mathematics of the Romanian Academy,Fakultät für Mathematik

[2] Universität Bielefeld,undefined

[3] Academy of Mathematic and System Sciences,undefined

[4] CAS,undefined

来源：

Stochastics and Partial Differential Equations: Analysis and Computations | 2021年 / 9卷

关键词：

Fokker–Planck equation; Mild solution; Distributional solution; 60H30; 60H10; 60G46; 35C99;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

One proves the uniqueness of distributional solutions to nonlinear Fokker–Planck equations with monotone diffusion term and derive as a consequence (restricted) uniqueness in law for the corresponding McKean–Vlasov stochastic differential equation (SDE).

引用

页码：702 / 713

页数：11

共 9 条

[1] Correction to: Uniqueness for nonlinear Fokker–Planck equations and weak uniqueness for McKean-Vlasov SDEs
Viorel Barbu
Michael Röckner
Stochastics and Partial Differential Equations: Analysis and Computations, 2023, 11 : 426 - 431
[2] Uniqueness for nonlinear Fokker-Planck equations and weak uniqueness for McKean-Vlasov SDEs
Barbu, Viorel
Roeckner, Michael
STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS, 2021, 9 (03): : 702 - 713
[3] Uniqueness for nonlinear Fokker-Planck equations and weak uniqueness for McKean-Vlasov SDEs (vol 9, pg 702, 2020)
Barbu, Viorel
Rockner, Michael
STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS, 2023, 11 (01): : 426 - 431
[4] Uniqueness for nonlinear Fokker-Planck equations and for McKean-Vlasov SDEs: The degenerate case
Barbu, Viorel
Roeckner, Michael
JOURNAL OF FUNCTIONAL ANALYSIS, 2023, 285 (04)
[5] Nonlinear Fokker-Planck equations with fractional Laplacian and McKean-Vlasov SDEs with Lévy noise
Barbu, Viorel
Roeckner, Michael
PROBABILITY THEORY AND RELATED FIELDS, 2024, 189 (3-4) : 849 - 878
[6] Generalized Solutions to Nonlinear Fokker-Planck Equations with Linear Drift
Barbu, Viorel
STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS AND RELATED FIELDS: IN HONOR OF MICHAEL ROCKNER, SPDERF, 2018, 229 : 293 - 302
[7] EXISTENCE OF OPTIMAL CONTROL FOR NONLINEAR FOKKER-PLANCK EQUATIONS IN L\bfone(RD).*
Barbu, Viorel
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2023, 61 (03) : 1213 - 1230
[8] Existence and uniqueness of solutions of nonlinear elliptic equations without growth conditions at infinity
Salomón Alarcón
Jorge García-Melián
Alexander Quaas
Journal d'Analyse Mathématique, 2012, 118 : 83 - 104
[9] Uniqueness of Mild Solutions to the Navier-Stokes Equations in Weak-type Ld\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^d$$\end{document} Space
Zhirun Zhan
Journal of Mathematical Fluid Mechanics, 2025, 27 (3)

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