Fractional Sobolev norms and BV functions on manifolds
Functional Analysis
2018-06-08 v2 Analysis of PDEs
Metric Geometry
Abstract
The bounded variation seminorm and the Sobolev seminorm on compact manifolds are represented as a limit of fractional Sobolev seminorms. This establishes a characterization of functions of bounded variation and of Sobolev functions on compact manifolds. As an application the special case of sets of finite perimeter is considered.
Keywords
Cite
@article{arxiv.1805.04425,
title = {Fractional Sobolev norms and BV functions on manifolds},
author = {Andreas Kreuml and Olaf Mordhorst},
journal= {arXiv preprint arXiv:1805.04425},
year = {2018}
}
Comments
changes from previous version: case p > 1 included, Lemma 2.2 added for clarification, typos corrected