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Mathematische Annalen

, Volume 350, Issue 1, pp 169–197 | Cite as

Sharp convex Lorentz–Sobolev inequalities

  • Monika Ludwig
  • Jie XiaoEmail author
  • Gaoyong Zhang
Article

Abstract

New sharp Lorentz–Sobolev inequalities are obtained by convexifying level sets in Lorentz integrals via the L p Minkowski problem. New L p 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.

Mathematics Subject Classification (2000)

26D 46E 52A 53C 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of MathematicsPolytechnic Institute of NYUBrooklynUSA
  2. 2.Department of Mathematics and StatisticsMemorial UniversitySt. John’sCanada

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