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

Augusto C. Ponce
, Daniel Eli Spector

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5 引文斯高帕斯（Scopus）

摘要

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.

貢獻的翻譯標題	A note on the fractional perimeter and interpolation
原文	English
頁（從 - 到）	960-965
頁數	6
期刊	Comptes Rendus Mathematique
卷	355
發行號	9
DOIs	https://doi.org/10.1016/j.crma.2017.09.001
出版狀態	Published - 9月 2017

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10.1016/j.crma.2017.09.001

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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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A note on the fractional perimeter and interpolation

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