Calculus of Variations and Geometric Measure Theory
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M. Miranda Jr

Functions of Bounded Variation on "good" Metric Spaces

created on 07 Jun 2000
modified by miranda on 20 Feb 2008


Published Paper

Inserted: 7 jun 2000
Last Updated: 20 feb 2008

Journal: J. Math. Pures Appl.
Volume: (9) 82
Number: 8
Pages: 975-1004
Year: 2003


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.


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