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 of order .
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}
}