The variational 1-capacity and BV functions with zero boundary values on metric spaces
Metric Geometry
2017-08-31 v1
Abstract
In the setting of a metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we define and study a class of BV functions with zero boundary values. In particular, we show that the class is the closure of compactly supported BV functions in the BV norm. Utilizing this theory, we then study the variational 1-capacity and its Lipschitz and BV analogs. We show that each of these is an outer capacity, and that the different capacities are equal for certain sets.
Keywords
Cite
@article{arxiv.1708.09318,
title = {The variational 1-capacity and BV functions with zero boundary values on metric spaces},
author = {Panu Lahti},
journal= {arXiv preprint arXiv:1708.09318},
year = {2017}
}