Improved Poincare inequalities with weights

被引：30

作者：

Drelichman, Irene ^{[1
]}

Duran, Ricardo G. ^{[1
]}

机构：

[1] Univ Buenos Aires, Fac Ciencias Exactas & Nat, Dept Matemat, RA-1428 Buenos Aires, DF, Argentina

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2008年 / 347卷 / 01期

关键词：

weighted Sobolev inequality; weighted Poincare inequality; reverse doubling weights; John domains;

D O I：

10.1016/j.jmaa.2008.06.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we prove that if Omega is an element of R-n is a bounded John domain, the following weighted Poincare-type inequality holds: [GRAPHICS] where f is a locally Lipschitz function on Omega, d(x) denotes the distance of x to the boundary of Omega, the weights W-1, W-2 satisfy certain cube conditions, and alpha is an element of [0, 1] depends on p, q and n. This result generalizes previously known weighted inequalities, which can also be obtained with our approach. (c) 2008 Elsevier Inc. All rights reserved.

引用

页码：286 / 293

页数：8

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