The variational 1-capacity and BV functions with zero boundary values on doubling metric spaces-Reference-Cited by-同舟云学术

The variational 1-capacity and BV functions with zero boundary values on doubling metric spaces

Published:2018-10-21 Issue:2 Volume:14 Page:171-192
ISSN:1864-8266
Container-title:Advances in Calculus of Variations
language:en
Short-container-title:

Author:

Lahti Panu¹

Affiliation:

1. Department of Mathematics , Linköping University , SE-581 83 Linköping , Sweden

Abstract

Abstract In the setting of a metric space that is equipped with a doubling measure and supports a Poincaré inequality, we define and study a class of BV

{\mathrm{BV}}

functions with zero boundary values. In particular, we show that the class is the closure of compactly supported BV

{\mathrm{BV}}

functions in the BV

{\mathrm{BV}}

norm. Utilizing this theory, we then study the variational 1-capacity and its Lipschitz and BV

{\mathrm{BV}}

analogs. We show that each of these is an outer capacity, and that the different capacities are equal for certain sets.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/acv-2018-0024/pdf

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