Improved Poincare inequalities with weights

被引：32
|
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.
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页码：286 / 293
页数：8
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