Weak uniqueness of Fokker-Planck equations with degenerate and bounded coefficients

Michael Röckner; Xicheng Zhang

doi:10.1016/j.crma.2010.01.001

Weak uniqueness of Fokker-Planck equations with degenerate and bounded coefficients

Michael Röckner^*, Xicheng Zhang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

34 Citations (Scopus)

Abstract

In this Note, by using the theory of stochastic differential equations (SDE), we prove uniqueness of measure-valued solutions and L^p-solutions to degenerate second order Fokker-Planck equations under weak conditions on the coefficients. Our uniqueness results are based on the natural connection between Fokker-Planck equations and SDEs.

Original language	English
Pages (from-to)	435-438
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	348
Issue number	7-8
DOIs	https://doi.org/10.1016/j.crma.2010.01.001
Publication status	Published - Apr 2010
Externally published	Yes

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10.1016/j.crma.2010.01.001

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title = "Weak uniqueness of Fokker-Planck equations with degenerate and bounded coefficients",

abstract = "In this Note, by using the theory of stochastic differential equations (SDE), we prove uniqueness of measure-valued solutions and Lp-solutions to degenerate second order Fokker-Planck equations under weak conditions on the coefficients. Our uniqueness results are based on the natural connection between Fokker-Planck equations and SDEs.",

author = "Michael R{\"o}ckner and Xicheng Zhang",

year = "2010",

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doi = "10.1016/j.crma.2010.01.001",

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AU - Zhang, Xicheng

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N2 - In this Note, by using the theory of stochastic differential equations (SDE), we prove uniqueness of measure-valued solutions and Lp-solutions to degenerate second order Fokker-Planck equations under weak conditions on the coefficients. Our uniqueness results are based on the natural connection between Fokker-Planck equations and SDEs.

AB - In this Note, by using the theory of stochastic differential equations (SDE), we prove uniqueness of measure-valued solutions and Lp-solutions to degenerate second order Fokker-Planck equations under weak conditions on the coefficients. Our uniqueness results are based on the natural connection between Fokker-Planck equations and SDEs.

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U2 - 10.1016/j.crma.2010.01.001

DO - 10.1016/j.crma.2010.01.001

M3 - Article

AN - SCOPUS:77949492590

SN - 1631-073X

VL - 348

SP - 435

EP - 438

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 7-8

ER -

Weak uniqueness of Fokker-Planck equations with degenerate and bounded coefficients

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