Sharp convex Lorentz-Sobolev inequalities

Monika Ludwig, Jie Xiao, Gaoyong Zhang

Research output: Contribution to journalArticle

Abstract

New sharp Lorentz-Sobolev inequalities are obtained by convexifying level sets in Lorentz integrals via the Lp Minkowski problem. New Lp isocapacitary and isoperimetric inequalities are proved for Lipschitz star bodies. It is shown that the sharp convex Lorentz-Sobolev inequalities are analytic analogues of isocapacitary and isoperimetric inequalities.

Original languageEnglish (US)
Pages (from-to)169-197
Number of pages29
JournalMathematische Annalen
Volume350
Issue number1
DOIs
StatePublished - May 2011

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Sobolev Inequality
Isoperimetric Inequality
Star Body
Level Set
Lipschitz
Analogue

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Sharp convex Lorentz-Sobolev inequalities. / Ludwig, Monika; Xiao, Jie; Zhang, Gaoyong.

In: Mathematische Annalen, Vol. 350, No. 1, 05.2011, p. 169-197.

Research output: Contribution to journalArticle

Ludwig, Monika ; Xiao, Jie ; Zhang, Gaoyong. / Sharp convex Lorentz-Sobolev inequalities. In: Mathematische Annalen. 2011 ; Vol. 350, No. 1. pp. 169-197.
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