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

DOI10.1007/s40072-020-00181-8zbMath1493.60107arXiv1909.04464OpenAlexW3083932450WikidataQ115375058 ScholiaQ115375058MaRDI QIDQ2062279

Viorel Barbu, Michael Roeckner

Publication date: 27 December 2021

Published in: Stochastic and Partial Differential Equations. Analysis and Computations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.04464

zbMATH Keywords

Fokker-Planck equationmild solutiondistributional solution

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Applications of stochastic analysis (to PDEs, etc.) (60H30) Representations of solutions to partial differential equations (35C99)

Related Items (11)

Linearization of nonlinear Fokker-Planck equations and applications ⋮ Nonlinear Fokker–Planck Equations with Time-Dependent Coefficients ⋮ Uniqueness for nonlinear Fokker-Planck equations and for McKean-Vlasov SDEs: the degenerate case ⋮ Well-posedness of density dependent SDE driven by \(\alpha \)-stable process with Hölder drifts ⋮ Existence of Optimal Control for Nonlinear Fokker–Planck Equations in \(\boldsymbol{L^1(\mathbb{R}^d)}\). ⋮ Stochastic Fokker–Planck Equations for Conditional McKean–Vlasov Jump Diffusions and Applications to Optimal Control ⋮ Controlling a generalized Fokker-Planck equation via inputs with nonlocal action ⋮ Correction to: ``Uniqueness for nonlinear Fokker-Planck equations and weak uniqueness for McKean-Vlasov SDEs ⋮ Euler scheme for density dependent stochastic differential equations ⋮ The invariance principle for nonlinear Fokker-Planck equations ⋮ The Trotter product formula for nonlinear Fokker-Planck flows

Cites Work

• Well-posedness of multidimensional diffusion processes with weakly differentiable coefficients
• Uniqueness for Fokker-Planck equations with measurable coefficients and applications to the fast diffusion equation
• Probabilistic representation for solutions of an irregular porous media type equation: The degenerate case
• From nonlinear Fokker-Planck equations to solutions of distribution dependent SDE
• Uniqueness of solutions of the initial-value problem for \(u_t- \Delta\varphi (u)=0\)
• Solutions for nonlinear Fokker-Planck equations with measures as initial data and Mckean-Vlasov equations
• Probabilistic Representation for Solutions to Nonlinear Fokker--Planck Equations
• Uniqueness of the solutions of ut−Δϕ(u) = 0 with initial datum a measure
• Nonlinear Differential Equations of Monotone Types in Banach Spaces

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