CSpace
Absolutely continuous solutions for continuity equations in Hilbert spaces
Da Prato, Giuseppe1; Flandoli, Franco1; Roeckner, Michael2,3
2019-08-01
Source PublicationJOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
ISSN0021-7824
Volume128Pages:42-86
AbstractWe prove existence of solutions to continuity equations in a separable Hilbert space. We look for solutions which are absolutely continuous with respect to a reference measure gamma which is Fomin-differentiable with exponentially integrable partial logarithmic derivatives. We describe a class of examples to which our result applies and for which we can prove also uniqueness. Finally, we consider the case where gamma is the invariant measure of a reaction-diffusion equation and prove uniqueness of solutions in this case. We exploit that the gradient operator D-x is closable with respect to L-p(H, gamma) and a recent formula for the commutator DxPt - PtDx where P-t is the transition semigroup corresponding to the reaction-diffusion equation, [10]. We stress that P-t is not necessarily symmetric in this case. This uniqueness result is an extension to such gamma of that in [12] where gamma was the Gaussian invariant measure of a suitable Ornstein-Uhlenbeck process. (C) 2019 Elsevier Masson SAS. All rights reserved.
KeywordContinuity equations Non Gaussian measures Rank condition
DOI10.1016/j.matpur.2019.06.010
Language英语
Funding ProjectGNAMPA from INdAM ; DFG[SFB 1283]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000480511900002
PublisherELSEVIER
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/35475
Collection中国科学院数学与系统科学研究院
Corresponding AuthorRoeckner, Michael
Affiliation1.Scuola Normale Super Pisa, Piazza Cavalieri 7, I-56126 Pisa, Italy
2.Bielefeld Univ, Univ Str 25, D-33615 Bielefeld, Germany
3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Da Prato, Giuseppe,Flandoli, Franco,Roeckner, Michael. Absolutely continuous solutions for continuity equations in Hilbert spaces[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES,2019,128:42-86.
APA Da Prato, Giuseppe,Flandoli, Franco,&Roeckner, Michael.(2019).Absolutely continuous solutions for continuity equations in Hilbert spaces.JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES,128,42-86.
MLA Da Prato, Giuseppe,et al."Absolutely continuous solutions for continuity equations in Hilbert spaces".JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES 128(2019):42-86.
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