English

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