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 \(0 < \alpha < 1\).
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