On continuity equations in infinite dimensions with non-Gaussian reference measure

Kolesnikov AV, Röckner M (2014)
Journal of Functional Analysis 266(7): 4490-4537.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
Download
Es wurde kein Volltext hochgeladen. Nur Publikationsnachweis!
Autor/in
Kolesnikov, Alexander V.; Röckner, MichaelUniBi
Abstract / Bemerkung
Let gamma be a Gaussian measure on a locally convex space and H be the corresponding Cameron-Martin space. It has been recently shown by L. Ambrosio and A. Figalli that the linear first-order PDE div rho + div(gamma)(rho center dot b) = 0, p vertical bar(t=o) = rho o, where rho(o) center dot gamma is a probability measure, admits a weak solution, in particular, under the following assumptions: vertical bar vertical bar b vertical bar vertical bar(H) is an element of L-p (gamma), p > 1, exp(epsilon(div(gamma)b)_) is an element of L-1 (gamma). Applying transportation of measures via triangular maps we prove a similar result for a large class of non-Gaussian probability measures nu on R-infinity, under the main assumption that beta(i) is an element of boolean AND(n is an element of N) L-n(nu) for every i is an element of N, where beta, is the logarithmic derivative of v along the coordinate x(i). We also show uniqueness of the solution for a wide class of measures. This class includes uniformly log-concave Gibbs measures and certain product measures. (C) 2014 Elsevier Inc. All rights reserved.
Stichworte
Renormalized solution; Gibbs; Gaussian measures; Triangular mappings; Sobolev a-priori estimates; measures; Continuity equation
Erscheinungsjahr
2014
Zeitschriftentitel
Journal of Functional Analysis
Band
266
Ausgabe
7
Seite(n)
4490-4537
ISSN
0022-1236
Page URI
https://pub.uni-bielefeld.de/record/2673605

Zitieren

Kolesnikov AV, Röckner M. On continuity equations in infinite dimensions with non-Gaussian reference measure. Journal of Functional Analysis. 2014;266(7):4490-4537.
Kolesnikov, A. V., & Röckner, M. (2014). On continuity equations in infinite dimensions with non-Gaussian reference measure. Journal of Functional Analysis, 266(7), 4490-4537. doi:10.1016/j.jfa.2014.01.010
Kolesnikov, A. V., and Röckner, M. (2014). On continuity equations in infinite dimensions with non-Gaussian reference measure. Journal of Functional Analysis 266, 4490-4537.
Kolesnikov, A.V., & Röckner, M., 2014. On continuity equations in infinite dimensions with non-Gaussian reference measure. Journal of Functional Analysis, 266(7), p 4490-4537.
A.V. Kolesnikov and M. Röckner, “On continuity equations in infinite dimensions with non-Gaussian reference measure”, Journal of Functional Analysis, vol. 266, 2014, pp. 4490-4537.
Kolesnikov, A.V., Röckner, M.: On continuity equations in infinite dimensions with non-Gaussian reference measure. Journal of Functional Analysis. 266, 4490-4537 (2014).
Kolesnikov, Alexander V., and Röckner, Michael. “On continuity equations in infinite dimensions with non-Gaussian reference measure”. Journal of Functional Analysis 266.7 (2014): 4490-4537.