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

數學系

研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

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.

原文	英語
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	已發佈 - 2017 9月

ASJC Scopus subject areas

一般數學

存取文件

10.1016/j.crma.2017.09.001

其它文件與鏈接

引用此

@article{7d071c92da4f4bf6a7d98673dd15056d,

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.",

author = "Ponce, {Augusto C.} and Daniel Spector",

note = "Publisher Copyright: {\textcopyright} 2017 Acad{\'e}mie des sciences",

year = "2017",

month = sep,

doi = "10.1016/j.crma.2017.09.001",

language = "English",

volume = "355",

pages = "960--965",

journal = "Comptes Rendus Mathematique",

issn = "1631-073X",

publisher = "Academie des sciences",

number = "9",

}

TY - JOUR

T1 - A note on the fractional perimeter and interpolation

AU - Ponce, Augusto C.

AU - Spector, Daniel

PY - 2017/9

Y1 - 2017/9

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=85030029986&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85030029986&partnerID=8YFLogxK

U2 - 10.1016/j.crma.2017.09.001

DO - 10.1016/j.crma.2017.09.001

M3 - Article

AN - SCOPUS:85030029986

SN - 1631-073X

VL - 355

SP - 960

EP - 965

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 9

ER -

A note on the fractional perimeter and interpolation

摘要

ASJC Scopus subject areas

存取文件

其它文件與鏈接

指紋

引用此