Sharp affine Lp Sobolev inequalities

Research output: Contribution to journalArticle

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 ℝp.

Original languageEnglish (US)
Pages (from-to)17-38
Number of pages22
JournalJournal of Differential Geometry
Volume62
Issue number1
StatePublished - Sep 2002

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Sobolev Inequality
Conformal Structure
Lebesgue Measure
Scalar, inner or dot product
Affine transformation
Vector space
Euclidean
Norm
Imply
Invariant

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis
  • Geometry and Topology

Cite this

Sharp affine Lp Sobolev inequalities. / Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong.

In: Journal of Differential Geometry, Vol. 62, No. 1, 09.2002, p. 17-38.

Research output: Contribution to journalArticle

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