Fokker-Planck equations and maximal dissipativity for Kolmogorov operators with time dependent singular drifts in Hilbert spaces
type: Item
instance of: scholarly article
title: Fokker-Planck equations and maximal dissipativity for Kolmogorov operators with time dependent singular drifts in Hilbert spaces
zbMATH Open document ID: 1161.47027
author: Vladimir I. Bogachev
author: Guiseppe Da Prato
author: Michael Röckner
published in: Journal of Functional Analysis
publication date: 2009-02-25T00:00:00Z
review text: The authors consider a Kolmogorov operator \(L_0\) in a Hilbert space H, related to a stochastic PDE with a singular quasi-dissipative drift \(F\) defined on a suitable space of regular functions. The authors prove that \(L_0\) is essentially \(m\)-dissipative in the space \(L^p\) with respect to a family of measures \(\nu_t\) that of the Fokker-Planck equation given by \(L_0\). This result implies that \(L_0\) generates a Markov \(C_0\) semigroup. A uniqueness result is also proved. Such results generalize previous ones obtained by the authors in the case of finite-dimensional spaces.
reviewed by: Vincenzo Vespri
Mathematics Subject Classification ID: 47D07
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 35K10
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35R60
zbMATH DE Number: 5518750
zbMATH Keywords: Kolmogorov operators
zbMATH Keywords: stochastic PDEs
zbMATH Keywords: singular coefficients
zbMATH Keywords: parabolic equations for measures
zbMATH Keywords: Fokker-Planck equations
zbMATH Keywords: maximal dissipativity
MaRDI profile type: Publication
full work available at URL: j.jfa.2008.05.005
OpenAlex ID: W2077000891
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DOI: 10.1016/J.JFA.2008.05.005
description: scientific article; zbMATH DE number 5518750