Sharp convex Lorentz-Sobolev inequalities

Monika Ludwig; Jie Xiao; Gaoyong Zhang

doi:10.1007/s00208-010-0555-x

Sharp convex Lorentz-Sobolev inequalities

Monika Ludwig, Jie Xiao, Gaoyong Zhang

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	169-197
Number of pages	29
Journal	Mathematische Annalen
Volume	350
Issue number	1
DOIs	https://doi.org/10.1007/s00208-010-0555-x
State	Published - May 2011

ASJC Scopus subject areas

General Mathematics

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10.1007/s00208-010-0555-x

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title = "Sharp convex Lorentz-Sobolev inequalities",

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.",

author = "Monika Ludwig and Jie Xiao and Gaoyong Zhang",

year = "2011",

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doi = "10.1007/s00208-010-0555-x",

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journal = "Mathematische Annalen",

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AU - Xiao, Jie

AU - Zhang, Gaoyong

PY - 2011/5

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N2 - 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.

AB - 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.

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Sharp convex Lorentz-Sobolev inequalities

Abstract

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