Moser-Trudinger inequalities without boundary conditions and isoperimetric problems

被引：55
|
作者：
Cianchi, A [1 ]
机构：
[1] Univ Florence, Dipartimento Matemat & Applicaz Architettura, I-50122 Florence, Italy
来源：
INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2005年 / 54卷 / 03期
关键词：
Sobolev inequalities; sharp constants; relative isoperimetric inequalites; rearrangements;
D O I：
10.1512/iumj.2005.54.2589
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The best constant is exhibited in Trudinger's exponential inequality for functions from the Sobolev space W-1,W-n (Omega), with Omega subset of R-n and n >= 2. This complements a classical result by Moser dealing with the subspace W-0(1,n) (Omega). An extension to the borderline Lorentz-Sobolev spaces (WLn,q)-L-1 (Omega) with 1 < q <= infinity is also established. A key step in our proofs is an asymptotically sharp relative isoperimetric inequality for domains in Rn.
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页码：669 / 705
页数：37
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