A note on the fractional perimeter and interpolation

Augusto C. Ponce; Daniel Spector

doi:10.1016/j.crma.2017.09.001

A note on the fractional perimeter and interpolation

Augusto C. Ponce
, Daniel Spector

Department of Mathematics

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

5 Citations (Scopus)

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.

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
Publication status	Published - 2017 Sept

ASJC Scopus subject areas

General Mathematics

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10.1016/j.crma.2017.09.001

Cite this

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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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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

AN - SCOPUS:85030029986

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EP - 965

JO - Comptes Rendus Mathematique

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A note on the fractional perimeter and interpolation

Abstract

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