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Existence and Uniqueness of Solutions to Fokker–Planck Type Equations with Irregular Coefficients

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Date
2008
Dewey
Probabilités et mathématiques appliquées
Sujet
Renormalized solutions; Linear transport equations; Kolmogorov equations; Fokker–Planck equations; DiPerna–Lions theory
Journal issue
Communications in Partial Differential Equations
Volume
33
Number
7
Publication date
2008
Article pages
1272-1317
Publisher
Taylor & Francis
DOI
http://dx.doi.org/10.1080/03605300801970952
URI
https://basepub.dauphine.fr/handle/123456789/8305
Collections
  • CEREMADE : Publications
Metadata
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Author
Lions, Pierre-Louis
Le Bris, Claude
Type
Article accepté pour publication ou publié
Abstract (EN)
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 1, p . Our arguments are based upon the DiPerna–Lions theory of renormalized solutions to linear transport equations and related equations [5]. The present work extends the results of our previous article [14], where only the simpler case of a Fokker–Planck equation with constant diffusion matrix was addressed. The consequences of the present results on the well-posedness of the associated stochastic differential equations are only outlined here. They will be more thoroughly examined in a forthcoming work [15].

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