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.

引用

页码：669 / 705

页数：37

共 43 条

[1] A SHARP INEQUALITY OF MOSER,J. FOR HIGHER-ORDER DERIVATIVES [J].