A note on the fractional perimeter and interpolation

Augusto C. Ponce; Daniel Eli Spector

doi:10.1016/j.crma.2017.09.001

A note on the fractional perimeter and interpolation

Translated title of the contribution: A note on the fractional perimeter and interpolation

Augusto C. Ponce, Daniel Eli Spector

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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^α,1 of order 0<α<1.

Translated title of the contribution	A note on the fractional perimeter and interpolation
Original language	English
Pages (from-to)	960-965
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	355
Issue number	9
DOIs	https://doi.org/10.1016/j.crma.2017.09.001
State	Published - Sep 2017

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10.1016/j.crma.2017.09.001

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title = "A note on the fractional perimeter and interpolation",

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,1 of order 0<α<1.",

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AU - Spector, Daniel Eli

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AB - 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,1 of order 0<α<1.

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DO - 10.1016/j.crma.2017.09.001

M3 - Article

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VL - 355

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JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

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A note on the fractional perimeter and interpolation

Abstract

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