Quasiopen sets, bounded variation and lower semicontinuity in metric spaces
Metric Geometry
2017-03-16 v1
Abstract
In the setting of a metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we show that the total variation of functions of bounded variation is lower semicontinuous with respect to -convergence in every -quasiopen set. To achieve this, we first prove a new characterization of the total variation in -quasiopen sets. Then we utilize the lower semicontinuity to show that the variation measures of a sequence of functions of bounded variation converging in the strict sense are uniformly absolutely continuous with respect to the -capacity.
Keywords
Cite
@article{arxiv.1703.04675,
title = {Quasiopen sets, bounded variation and lower semicontinuity in metric spaces},
author = {Panu Lahti},
journal= {arXiv preprint arXiv:1703.04675},
year = {2017}
}