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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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/875245 |
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| _version_ | 1849400209415602176 |
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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. |
| format | Article |
| id | doaj-art-a0c788f8fbc24caa992f923d3d5a794f |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| 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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