English

On Hausdorff measure and an inequality due to Maz'ya

Functional Analysis 2021-01-19 v3

Abstract

We give an "elementary" proof of an inequality due to Maz'ya. As a prerequisite we prove an approximation property for the Hausdorff measure. We also comment on the relations between Maz'ya's inequality, the isoperimetric inequality and the Sobolev inequality.

Keywords

Cite

@article{arxiv.1910.07837,
  title  = {On Hausdorff measure and an inequality due to Maz'ya},
  author = {Hendrik Vogt and Jürgen Voigt},
  journal= {arXiv preprint arXiv:1910.07837},
  year   = {2021}
}