Some fine properties of sets with finite perimeter in Wiener spaces

• Autorzy: Michele Miranda Jr.
• Języki publikacji: EN

Abstrakty

EN

In this paper we give a brief overview on the state of art of developments of Geometric Measure Theory in infinite-dimensional Banach spaces. The framework is given by an abstract Wiener space, that is a separable Banach space endowed with a centered Gaussian measure. The focus of the paper is on the theory of sets with finite perimeter and on their properties; this choice was motivated by the fact that most of the good properties of functions of bounded variation can be obtained, thanks to coarea formula, from the geometric properties of sets with finite perimeter.

Kategorie tematyczne

• 26E15: Calculus of functions on infinite-dimensional spaces
• 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
• 49Q15: Geometric measure and integration theory, integral and normal currents
• 60H07: Stochastic calculus of variations and the Malliavin calculus

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2014
• Tom: 101
• Numer: 1
• Strony: 115-125

Daty

wydano

2014

Twórcy

autor

Michele Miranda Jr.

• Department of Mathematics and Computer Science, University of Ferrara, via Machiavelli 35, I-44121 Ferrara, Italy

Identyfikatory

DOI

10.4064/bc101-0-9