The Pólya-Szegö Principle and the Anisotropic Convex Lorentz-Sobolev Inequality

An anisotropic convex Lorentz-Sobolev inequality is established, which extends Ludwig, Xiao, and Zhang’s result to any norm from Euclidean norm, and the geometric analogue of this inequality is given. In addition, it implies that the (anisotropic) Pólya-Szegö principle is shown.

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Main Authors: Shuai Liu, Binwu He
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:The Scientific World Journal
Online Access:http://dx.doi.org/10.1155/2014/875245
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author Shuai Liu
Binwu He
author_facet Shuai Liu
Binwu He
author_sort Shuai Liu
collection DOAJ
description An anisotropic convex Lorentz-Sobolev inequality is established, which extends Ludwig, Xiao, and Zhang’s result to any norm from Euclidean norm, and the geometric analogue of this inequality is given. In addition, it implies that the (anisotropic) Pólya-Szegö principle is shown.
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institution Kabale University
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spelling doaj-art-a0c788f8fbc24caa992f923d3d5a794f2025-08-20T03:38:08ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/875245875245The Pólya-Szegö Principle and the Anisotropic Convex Lorentz-Sobolev InequalityShuai Liu0Binwu He1Department of Mathematics, Shanghai University, Shanghai 200444, ChinaDepartment of Mathematics, Shanghai University, Shanghai 200444, ChinaAn anisotropic convex Lorentz-Sobolev inequality is established, which extends Ludwig, Xiao, and Zhang’s result to any norm from Euclidean norm, and the geometric analogue of this inequality is given. In addition, it implies that the (anisotropic) Pólya-Szegö principle is shown.http://dx.doi.org/10.1155/2014/875245
spellingShingle Shuai Liu
Binwu He
The Pólya-Szegö Principle and the Anisotropic Convex Lorentz-Sobolev Inequality
The Scientific World Journal
title The Pólya-Szegö Principle and the Anisotropic Convex Lorentz-Sobolev Inequality
title_full The Pólya-Szegö Principle and the Anisotropic Convex Lorentz-Sobolev Inequality
title_fullStr The Pólya-Szegö Principle and the Anisotropic Convex Lorentz-Sobolev Inequality
title_full_unstemmed The Pólya-Szegö Principle and the Anisotropic Convex Lorentz-Sobolev Inequality
title_short The Pólya-Szegö Principle and the Anisotropic Convex Lorentz-Sobolev Inequality
title_sort polya szego principle and the anisotropic convex lorentz sobolev inequality
url http://dx.doi.org/10.1155/2014/875245
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