Sharp affine LP sobolev inequalities

Erwin Lutwak, Deane Yang, Gaoyong Zhang

Research output: Contribution to journalArticlepeer-review


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.

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

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology


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