Absolutely continuous solutions for continuity equations in Hilbert spaces

Da Prato G, Flandoli F, Röckner M (2019)
Journal de Mathématiques Pures et Appliquées 128: 42-86.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Download
Es wurde kein Volltext hochgeladen. Nur Publikationsnachweis!
Autor/in
; ;
Abstract / Bemerkung
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.
Stichworte
Continuity equations; Non Gaussian measures; Rank condition
Erscheinungsjahr
2019
Zeitschriftentitel
Journal de Mathématiques Pures et Appliquées
Band
128
Seite(n)
42-86
ISSN
0021-7824
eISSN
1776-3371
Page URI
https://pub.uni-bielefeld.de/record/2937112

Zitieren

Da Prato G, Flandoli F, Röckner M. Absolutely continuous solutions for continuity equations in Hilbert spaces. Journal de Mathématiques Pures et Appliquées. 2019;128:42-86.
Da Prato, G., Flandoli, F., & Röckner, M. (2019). Absolutely continuous solutions for continuity equations in Hilbert spaces. Journal de Mathématiques Pures et Appliquées, 128, 42-86. doi:10.1016/j.matpur.2019.06.010
Da Prato, G., Flandoli, F., and Röckner, M. (2019). Absolutely continuous solutions for continuity equations in Hilbert spaces. Journal de Mathématiques Pures et Appliquées 128, 42-86.
Da Prato, G., Flandoli, F., & Röckner, M., 2019. Absolutely continuous solutions for continuity equations in Hilbert spaces. Journal de Mathématiques Pures et Appliquées, 128, p 42-86.
G. Da Prato, F. Flandoli, and M. Röckner, “Absolutely continuous solutions for continuity equations in Hilbert spaces”, Journal de Mathématiques Pures et Appliquées, vol. 128, 2019, pp. 42-86.
Da Prato, G., Flandoli, F., Röckner, M.: Absolutely continuous solutions for continuity equations in Hilbert spaces. Journal de Mathématiques Pures et Appliquées. 128, 42-86 (2019).
Da Prato, Giuseppe, Flandoli, Franco, and Röckner, Michael. “Absolutely continuous solutions for continuity equations in Hilbert spaces”. Journal de Mathématiques Pures et Appliquées 128 (2019): 42-86.