| 优化Sobolev体及其仿射性质 |
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| 引用本文： | 吴力荣.优化Sobolev体及其仿射性质[J].应用数学与计算数学学报,2012,26(2):185-192. |
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| 作者姓名： | 吴力荣 |
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| 作者单位： | 浙江工业职业技术学院,浙江绍兴,312000 |
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| 基金项目： | 基金项目:国家自然科学基金资助项目 |
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| 摘 要： | Sobolev不等式是联系分析和几何的基础不等式之一,而优化Sobolev体是优化Sobolev范数的临界几何核.首先,证明优化Sobolev体的一些仿射性质.然后,运用Barthe的优化迁移方法研究了凸体的特征函数和多胞形仿射函数的优化Sobolev体.
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| 关 键 词： | Sobolev空间 优化Sobolev体 Sobolev不等式 Minkowski问题 |
Optimal Sobolev bodies and their affine properties |
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| WU Li-rong.Optimal Sobolev bodies and their affine properties[J].Communication on Applied Mathematics and Computation,2012,26(2):185-192. |
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| Authors: | WU Li-rong |
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| Institution: | WU Li-rong (Zhejiang Industry Polytechnic College,Shaoxing 312000,Zhejiang Province,China) |
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| Abstract: | The Sobolev inequality is one of the fundamental inequalities connecting analysis and geometry,and optimal Sobolev bodies are the critical geometric kernel of the Sobolev norms.Some affine properties of the optimal Sobolev bodies have been proved firstly,and then the optimal Sobolev bodies for characteristic functions of convex bodies and piecewise affine functions of polytopes are investigated by an optimal transport approach of Barthe. |
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| Keywords: | Sobolev space optimal Sobolev body Sobolev inequality Minkowskiproblem |
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