径向密度等周不等式的极限情况及其应用

IF 0.7 4区数学 Q2 MATHEMATICS

Communications in Analysis and Geometry Pub Date : 2019-12-27 DOI:10.4310/cag.2022.v30.n6.a6

Georgios Psaradakis

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引用次数: 0

摘要

我们证明了一个具有径向密度的尖锐等周不等式，其函数对偶对应于L 1中Il'in(或Caffarelli-Kohn-Nirenberg)不等式指数的极限情况。我们展示了后者如何应用于[25]的L 1加权Hardy不等式之一的最优临界Sobolev加权范数改进。进一步的应用包括具有该等环不等式的最佳常数的泛函类似的L - p版本以及加权的Polya-Szego不等式。

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Limiting case of an isoperimetric inequality with radial densities and applications

We prove a sharp isoperimetric inequality with radial density whose functional counterpart corresponds to a limiting case for the exponents of the Il'in (or Caffarelli-Kohn-Nirenberg) inequality in L 1. We show how the latter applies to obtain an optimal critical Sobolev weighted norm improvement to one of the L 1 weighted Hardy inequalities of [25]. Further applications include an L p version with the best constant of the functional analogue of this isoperimetric inequality and also a weighted Polya-Szego inequality.

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来源期刊

Communications in Analysis and Geometry 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes high-quality papers on subjects related to classical analysis, partial differential equations, algebraic geometry, differential geometry, and topology.