KMS Of Academy of mathematics and systems sciences, CAS
Absolutely continuous solutions for continuity equations in Hilbert spaces | |
Da Prato, Giuseppe1; Flandoli, Franco1; Roeckner, Michael2,3 | |
2019-08-01 | |
Source Publication | JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES |
ISSN | 0021-7824 |
Volume | 128Pages:42-86 |
Abstract | We 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. |
Keyword | Continuity equations Non Gaussian measures Rank condition |
DOI | 10.1016/j.matpur.2019.06.010 |
Language | 英语 |
Funding Project | GNAMPA from INdAM ; DFG[SFB 1283] |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000480511900002 |
Publisher | ELSEVIER |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/35475 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Roeckner, Michael |
Affiliation | 1.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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