Sharp convex Lorentz-Sobolev inequalities

Monika Ludwig, Jie Xiao, Gaoyong Zhang

Research output: Contribution to journalArticlepeer-review


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
Issue number1
StatePublished - May 2011

ASJC Scopus subject areas

  • General Mathematics


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