Existence and Uniqueness of Solutions to Fokker–Planck Type Equations with Irregular Coefficients
Lions, Pierre-Louis; Le Bris, Claude (2008), Existence and Uniqueness of Solutions to Fokker–Planck Type Equations with Irregular Coefficients, Communications in Partial Differential Equations, 33, 7, p. 1272-1317. http://dx.doi.org/10.1080/03605300801970952
TypeArticle accepté pour publication ou publié
Journal nameCommunications in Partial Differential Equations
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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 . The present work extends the results of our previous article , 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 .
Subjects / KeywordsRenormalized solutions; Linear transport equations; Kolmogorov equations; Fokker–Planck equations; DiPerna–Lions theory
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