Balls have the worst best Sobolev inequalities
Balls have the worst best Sobolev inequalities
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球具有最差、最好的索博列夫不等式
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
C. Villani
中科院分区：
文献类型：
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作者：
F. Maggi;C. Villani
利用Cordero-Erausquin，Nazaret和Villani [7]中的迁移技巧，我们对任意局部Lipschitz整环建立了一个最优非参数迹Sobolev不等式.本文导出了Brézis-Lieb迹Sobolev不等式的一个尖锐变形，其中包含了等周不等式和尖锐的欧氏Sobolev嵌入.这个不等式对于球是最优的，并且对于任何其他有界Lipschitz连通域都可以得到改进。我们还得到了Brézis-Lieb不等式的一个加强，该不等式在[4]中被建议并作为一个开放问题。许多变体将在配套文章中进行研究[10]。
Using transportation techniques in the spirit of Cordero-Erausquin, Nazaret and Villani [7], we establish an optimal non parametric trace Sobolev inequality, for arbitrary locally Lipschitz domains in ℝn. We deduce a sharp variant of the Brézis-Lieb trace Sobolev inequality [4], containing both the isoperimetric inequality and the sharp Euclidean Sobolev embedding as particular cases. This inequality is optimal for a ball, and can be improved for any other bounded, Lipschitz, connected domain. We also derive a strengthening of the Brézis-Lieb inequality, suggested and left as an open problem in [4]. Many variants will be investigated in a companion article [10].