# A note on the Fractional Perimeter and Interpolation

created by spector on 19 Jul 2017

[BibTeX]

Preprint

Inserted: 19 jul 2017
Last Updated: 19 jul 2017

Year: 2017

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 $W^{\alpha, 1}$ of order $0 < \alpha < 1$.