From Brunn-Minkowski to sharp Sobolev inequalities

S. G. Bobkov; M. Ledoux

doi:10.1007/s10231-007-0047-0

From Brunn-Minkowski to sharp Sobolev inequalities

S. G. Bobkov, M. Ledoux

School of Mathematics

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

26 Scopus citations

Abstract

We present a simple direct proof of the classical Sobolev inequality in ℝ with best constant from the geometric Brunn-Minkowski-Lusternik inequality.

Original language	English (US)
Pages (from-to)	369-384
Number of pages	16
Journal	Annali di Matematica Pura ed Applicata
Volume	187
Issue number	3
DOIs	https://doi.org/10.1007/s10231-007-0047-0
State	Published - Jul 2008

Bibliographical note

Funding Information:
Research supported in part by NSF Gr. No. 0405587 and B. Zegarlinski’s Pierre de Fermat Grant 2006 from the Région Midi-Pyrénées, France.

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10.1007/s10231-007-0047-0

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title = "From Brunn-Minkowski to sharp Sobolev inequalities",

abstract = "We present a simple direct proof of the classical Sobolev inequality in ℝ with best constant from the geometric Brunn-Minkowski-Lusternik inequality.",

author = "Bobkov, \{S. G.\} and M. Ledoux",

note = "Funding Information: Research supported in part by NSF Gr. No. 0405587 and B. Zegarlinski{\textquoteright}s Pierre de Fermat Grant 2006 from the R{\'e}gion Midi-Pyr{\'e}n{\'e}es, France.",

year = "2008",

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doi = "10.1007/s10231-007-0047-0",

language = "English (US)",

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AU - Bobkov, S. G.

AU - Ledoux, M.

N1 - Funding Information: Research supported in part by NSF Gr. No. 0405587 and B. Zegarlinski’s Pierre de Fermat Grant 2006 from the Région Midi-Pyrénées, France.

PY - 2008/7

Y1 - 2008/7

N2 - We present a simple direct proof of the classical Sobolev inequality in ℝ with best constant from the geometric Brunn-Minkowski-Lusternik inequality.

AB - We present a simple direct proof of the classical Sobolev inequality in ℝ with best constant from the geometric Brunn-Minkowski-Lusternik inequality.

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VL - 187

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EP - 384

JO - Annali di Matematica Pura ed Applicata

JF - Annali di Matematica Pura ed Applicata

IS - 3

ER -

From Brunn-Minkowski to sharp Sobolev inequalities

Abstract

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