Published Paper
(2003)
Author:
Michele Miranda Jr
Journal: J. Math. Pures Appl. [MathSciNet]
Volume: (9) 82
Number: 8
Pages: 975-1004
Abstract:
In this paper we give a possible definition of the space
of Banach space valued BV functions on metric spaces; the
metric space is supposed to be doubling and that it supports
a Poincaré inequality. The idea of the definition of BV functions
is to take the closure with respect to a suitable convergence
of regular functions, the Lipschitz functions. The main problem
with this definition is the proof that the total variation
is a measure, and the techniques used are typical of the relaxation
analysis.
In this paper we also define the sets of finite perimeter and we
give some basic properties of this family of sets; the main
tool that we prove in this section is the
Coarea formula for BV functions.![[PS]](/style/ps.png)
![[PDF]](/style/pdf.png)
[BibTeX Entry]
Available Files:
abstract.tex (abstract.ps, abstract.pdf)
metricbv.ps (metricbv.pdf)
