Sharp affine LP sobolev inequalities

Erwin Lutwak; Deane Yang; Gaoyong Zhang

doi:10.4310/jdg/1090425527

Sharp affine L_P sobolev inequalities

Erwin Lutwak, Deane Yang, Gaoyong Zhang

Mathematics

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

Abstract

A sharp affine L_p Sobolev inequality for functions on Euclidean n-space is established. This new inequality is significantly stronger than (and directly implies) the classical sharp L_p Sobolev inequality of Aubin and Talenti, even though it uses only the vector space structure and standard Lebesgue measure on ℝ_n. For the new inequality, no inner product, norm, or conformal structure is needed; the inequality is invariant under all affine transformations of ℝ_n.

Original language	English (US)
Pages (from-to)	17-38
Number of pages	22
Journal	Journal of Differential Geometry
Volume	62
Issue number	1
DOIs	https://doi.org/10.4310/jdg/1090425527
State	Published - 2002

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology

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10.4310/jdg/1090425527

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title = "Sharp affine LP sobolev inequalities",

abstract = "A sharp affine Lp Sobolev inequality for functions on Euclidean n-space is established. This new inequality is significantly stronger than (and directly implies) the classical sharp Lp Sobolev inequality of Aubin and Talenti, even though it uses only the vector space structure and standard Lebesgue measure on ℝn. For the new inequality, no inner product, norm, or conformal structure is needed; the inequality is invariant under all affine transformations of ℝn.",

author = "Erwin Lutwak and Deane Yang and Gaoyong Zhang",

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AB - A sharp affine Lp Sobolev inequality for functions on Euclidean n-space is established. This new inequality is significantly stronger than (and directly implies) the classical sharp Lp Sobolev inequality of Aubin and Talenti, even though it uses only the vector space structure and standard Lebesgue measure on ℝn. For the new inequality, no inner product, norm, or conformal structure is needed; the inequality is invariant under all affine transformations of ℝn.

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Sharp affine L_P sobolev inequalities

Abstract

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