English

A note on the fractional perimeter and interpolation

Functional Analysis 2018-07-20 v1

Abstract

We present the fractional perimeter as a set-function interpolation between the Lebesgue measure and the perimeter in the sense of De Giorgi. Our motivation comes from a new fractional Boxing inequality that relates the fractional perimeter and the Hausdorff content and implies several known inequalities involving the Gagliardo seminorm of the Sobolev spaces Wα,1W^{\alpha, 1} of order 0<α<10 < \alpha < 1.

Keywords

Cite

@article{arxiv.1707.06001,
  title  = {A note on the fractional perimeter and interpolation},
  author = {Augusto C. Ponce and Daniel Spector},
  journal= {arXiv preprint arXiv:1707.06001},
  year   = {2018}
}
R2 v1 2026-06-22T20:51:26.857Z