POINCARÉ INEQUALITIES IN WEIGHTED SOBOLEV SPACES

doi:10.1007/s10483-006-0116-1

Applied Mathematics and Mechanics (English Edition) ›› 2006, Vol. 27 ›› Issue (1): 125-132 .doi: https://doi.org/10.1007/s10483-006-0116-1

POINCARÉ INEQUALITIES IN WEIGHTED SOBOLEV SPACES

王万义, 孙炯, 郑志明

收稿日期:2003-02-25 修回日期:2005-08-23 出版日期:2006-01-18 发布日期:2006-01-18
通讯作者: 王万义

POINCARÉ INEQUALITIES IN WEIGHTED SOBOLEV SPACES

WANG Wan-yi, SUN Jiong, ZHENG Zhi-ming

1. Department of Mathematics, Inner Mongolia University, Huhhot 010021, P.R.China;
2. Department of Mathematics, Inner Mongolia Normal University, Huhhot 010022, P.R.China;
3. School of Mathematical Sciences, Beijing University, Beijing 100871, P.R.China

Received:2003-02-25 Revised:2005-08-23 Online:2006-01-18 Published:2006-01-18
Contact: WANG Wan-yi

摘要/Abstract

Abstract: The weighted Poincaré inequalities in weighted Sobolev spaces are discussed, and the necessary and sufficient conditions for them to hold are given. That is, the Poincaré inequalities hold if, and only if, the ball measure of non-compactness of the natural embedding of weighted Sobolev spaces is less than 1.

Key words: weighted sobolev spaces, Poincaré inequalities, embeddings

中图分类号:

王万义;孙炯;郑志明. POINCARÉ INEQUALITIES IN WEIGHTED SOBOLEV SPACES[J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(1): 125-132 .

WANG Wan-yi;SUN Jiong;ZHENG Zhi-ming. POINCARÉ INEQUALITIES IN WEIGHTED SOBOLEV SPACES[J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(1): 125-132 .

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POINCARÉ INEQUALITIES IN WEIGHTED SOBOLEV SPACES

POINCARÉ INEQUALITIES IN WEIGHTED SOBOLEV SPACES

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