Calculus of Variations and Geometric Measure Theory

A. Ponce - D. Spector

A note on the Fractional Perimeter and Interpolation

created by spector on 19 Jul 2017



Inserted: 19 jul 2017
Last Updated: 19 jul 2017

Year: 2017


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 \(0 < \alpha < 1\).