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.

Detalles Bibliográficos
Autores principales: Liu, Shuai, He, Binwu
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4124251/
https://www.ncbi.nlm.nih.gov/pubmed/25136698
http://dx.doi.org/10.1155/2014/875245
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author Liu, Shuai
He, Binwu
author_facet Liu, Shuai
He, Binwu
author_sort Liu, Shuai
collection PubMed
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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spelling pubmed-41242512014-08-18 The Pólya-Szegö Principle and the Anisotropic Convex Lorentz-Sobolev Inequality Liu, Shuai He, Binwu ScientificWorldJournal Research Article 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. Hindawi Publishing Corporation 2014 2014-07-15 /pmc/articles/PMC4124251/ /pubmed/25136698 http://dx.doi.org/10.1155/2014/875245 Text en Copyright © 2014 S. Liu and B. He. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Liu, Shuai
He, Binwu
The Pólya-Szegö Principle and the Anisotropic Convex Lorentz-Sobolev Inequality
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 pólya-szegö principle and the anisotropic convex lorentz-sobolev inequality
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4124251/
https://www.ncbi.nlm.nih.gov/pubmed/25136698
http://dx.doi.org/10.1155/2014/875245
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