Uniqueness problems for degenerate Fokker-Planck-Kolmogorov equations

DOI10.1007/s10958-015-2362-0zbMath1321.35242OpenAlexW2022715537MaRDI QIDQ2515207

Stanislav V. Shaposhnikov, Vladimir I. Bogachev, Michael Roeckner

Publication date: 31 July 2015

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-015-2362-0

zbMATH Keywords

uniquenessFokker-Planck-Kolmogorov equation

Mathematics Subject Classification ID

Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) PDEs with randomness, stochastic partial differential equations (35R60) Stochastic integral equations (60H20) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Fokker-Planck equations (35Q84)

Related Items (10)

Distances between transition probabilities of diffusions and applications to nonlinear Fokker-Planck-Kolmogorov equations ⋮ Hardy-Littlewood-Sobolev inequalities for a class of non-symmetric and non-doubling hypoelliptic semigroups ⋮ The Itô SDEs and Fokker–Planck equations with Osgood and Sobolev coefficients ⋮ Fokker-Planck-Kolmogorov equations with a partially degenerate diffusion matrix ⋮ Quantification of coarse-graining error in Langevin and overdamped Langevin dynamics ⋮ Kolmogorov equations for degenerate Ornstein-Uhlenbeck operators ⋮ Quantitative stability estimates for Fokker-Planck equations ⋮ Stochastic nonlinear Fokker-Planck equations ⋮ On the Ambrosio-Figalli-Trevisan superposition principle for probability solutions to Fokker-Planck-Kolmogorov equations ⋮ On uniqueness of probability solutions of the Fokker-Planck-Kolmogorov equation

Cites Work

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• On the Cauchy problem for Fokker-Planck-Kolmogorov equations with potential terms on arbitrary domains
• On uniqueness of solutions to the Cauchy problem for degenerate Fokker-Planck-Kolmogorov equations
• \(L^p\)-solutions of Fokker-Planck equations
• Degenerate Fokker-Planck equations: Bismut formula, gradient estimate and Harnack inequality
• Uniqueness for Fokker-Planck equations with measurable coefficients and applications to the fast diffusion equation
• Uniqueness of degenerate Fokker-Planck equations with weakly differentiable drift whose gradient is given by a singular integral
• Ordinary differential equations, transport theory and Sobolev spaces
• Weak uniqueness of Fokker-Planck equations with degenerate and bounded coefficients
• Uniqueness of signed measures solving the continuity equation for Osgood vector fields
• Probabilistic representation and uniqueness results for measure-valued solutions of transport equations
• Existence of weak solutions of stochastic differential equations with discontinuous coefficients and with a partially degenerate diffusion operator
• Über die analytischen Methoden in der Wahrscheinlichkeitsrechnung
• Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients
• Well-posedness and large deviation for degenerate SDEs with Sobolev coefficients
• Probabilistic representation for solutions of an irregular porous media type equation
• On uniqueness problems related to the Fokker-Planck-Kolmogorov equation for measures
• Existence and uniqueness of martingale solutions for SDEs with rough or degenerate coefficients
• ON REGULARITY OF TRANSITION PROBABILITIES AND INVARIANT MEASURES OF SINGULAR DIFFUSIONS UNDER MINIMAL CONDITIONS
• On Uniqueness of a Probability Solution to the Cauchy Problem for the Fokker–Planck–Kolmogorov Equation
• The Fokker–Planck–Kolmogorov equations with a potential and a non-uniformly elliptic diffusion matrix
• An analytic approach to infinite-dimensional continuity and Fokker-Planck-Kolmogorov equations
• Existence and Uniqueness of Solutions to Fokker–Planck Type Equations with Irregular Coefficients
• Uniqueness of solutions to weak parabolic equations for measures
• On Parabolic Equations for Measures

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