Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/on-integration-by-parts-formula-on-open-convex-sets-in-wiener-spaces-86hDbHyOVv
References (26)
-
G. Cappa (2015)
On the Ornstein-Uhlenbeck operator in convex sets of Banach spacesarXiv: Analysis of PDEs
-
V. Caselles, A. Lunardi, Michele jr., M. Novaga (2011)
Perimeter of sublevel sets in infinite dimensional spacesAdvances in Calculus of Variations, 5
-
L. Ambrosio, D. Pallara, N. Fusco (2000)
Functions of Bounded Variation and Free Discontinuity Problems -
A. Lunardi, M. Miranda, D. Pallara (2014)
BV Functions on Convex Domains in Wiener SpacesPotential Analysis, 43
-
D. Feyel, A. Pradelle (1992)
Hausdorff measures on the Wiener spacePotential Analysis, 1
-
L. Ambrosio, M. Miranda, D. Pallara (2010)
Sets with finite perimeter in Wiener spaces, perimeter measure and boundary rectifiabilityDiscrete and Continuous Dynamical Systems, 28
-
L. Ambrosio, M. Miranda, Stefania Maniglia, D. Pallara (2010)
BV functions in abstract Wiener spacesJournal of Functional Analysis, 258
-
Helène Airault (1988)
3Bull. Sci. Math. (2), 112
-
M. Hino (2009)
Sets of finite perimeter and the Hausdorff-Gauss measure on the Wiener spaceJournal of Functional Analysis, 258
-
D. Addona, G. Menegatti, M. Miranda (2020)
\begin{document}$ BV $\end{document} functions on open domains: the Wiener case and a Fomin differentiable caseCommunications on Pure and Applied Analysis, 19
-
P. Celada, A. Lunardi (2013)
Traces of Sobolev functions on regular surfaces in infinite dimensionsarXiv: Analysis of PDEs
-
M. Fukushima (2000)
BV Functions and Distorted Ornstein Uhlenbeck Processes over the Abstract Wiener SpaceJournal of Functional Analysis, 174
-
Luigi Ambrosio, Michele Miranda, Diego Pallara (2015)
Some fine properties of BV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$BV$$\end{document} functions on Wiener spacesAnal. Geom. Metr. Spaces, 3
-
(1953)
Definizione ed espressione analitica del perimetro di un insieme -
S. Albeverio, Zhi-Ming Ma, M. Röckner (1997)
Partitions of Unity in Sobolev Spaces over Infinite Dimensional State SpacesJournal of Functional Analysis, 143
-
L. Ambrosio, Michele jr., D. Pallara (2015)
Some Fine Properties of BV Functions on Wiener SpacesAnalysis and Geometry in Metric Spaces, 3
-
D. Addona, G. Menegatti, M. Miranda, F. Wang (2020)
BV FUNCTIONS ON OPEN DOMAINS: THE WIENER CASE AND A FOMIN DIFFERENTIABLE CASE -
David Preiss (1981)
Gaussian measures and the density theoremComment. Math. Univ. Carolin., 22
-
(1988)
Functions of bounded variations on open domains in Wiener spaces . in preparation . [ 2 ] H . Airault and P . Malliavin . Intégration géométrique sur l ’ espace de Wiener -
L. Ambrosio, A. Figalli (2010)
Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spacesarXiv: Classical Analysis and ODEs
-
(1988)
Intégration géométriquesur l’espace deWiener -
Gaussian Measures on a -
M. Fukushima, M. Hino (2001)
On the Space of BV Functions and a Related Stochastic Calculus in Infinite DimensionsJournal of Functional Analysis, 183
-
R. Phelps (1989)
Convex Functions, Monotone Operators and Differentiability -
G. Cappa (2015)
Maximal $L^2$ regularity for Ornstein-Uhlenbeck equation in convex sets of Banach spacesarXiv: Analysis of PDEs
-
Ronald Gariepy (2001)
FUNCTIONS OF BOUNDED VARIATION AND FREE DISCONTINUITY PROBLEMS (Oxford Mathematical Monographs)Bulletin of The London Mathematical Society, 33
- Publisher
- Springer Journals
- Copyright
- Copyright © Springer Nature Switzerland AG 2021
- ISSN
- 1424-3199
- eISSN
- 1424-3202
- DOI
- 10.1007/s00028-020-00663-1
- Publisher site
- See Article on Publisher Site
Abstract
In Euclidean space, it is well known that any integration by parts formula for a set of finite perimeter Ω\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Omega $$\end{document} is expressed by the integration with respect to a measure P(Ω,·)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$P(\Omega ,\cdot )$$\end{document} which is equivalent to the one-codimensional Hausdorff measure restricted to the reduced boundary of Ω\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Omega $$\end{document}. The same result has been proved in an abstract Wiener space, typically an infinite-dimensional space, where the surface measure considered is the one-codimensional spherical Hausdorff–Gauss measure S∞-1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathscr {S}^{\infty -1}$$\end{document} restricted to the measure-theoretic boundary of Ω\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Omega $$\end{document}. In this paper, we consider an open convex set Ω\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Omega $$\end{document} and we provide an explicit formula for the density of P(Ω,·)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$P(\Omega ,\cdot )$$\end{document} with respect to S∞-1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathscr {S}^{\infty -1}$$\end{document}. In particular, the density can be written in terms of the Minkowski functional p\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathfrak {p}$$\end{document} of Ω\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Omega $$\end{document} with respect to an inner point of Ω\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Omega $$\end{document}. As a consequence, we obtain an integration by parts formula for open convex sets in Wiener spaces.
Journal
Journal of Evolution Equations – Springer Journals
Published: Jan 18, 2021
Keywords: Infinite-dimensional analysis; Abstract Wiener spaces; Integration by parts formula; Convex analysis; Geometric measure theory; Primary: 28C20; Secondary: 46G05; 46N10