POINCAR&Eacute; INEQUALITIES IN WEIGHTED SOBOLEV SPACES

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

doi:10.1007/s10483-006-0116-1

Applied Mathematics and Mechanics >

2006 , Vol. 27 >Issue 1: 125 - 132

DOI: https://doi.org/10.1007/s10483-006-0116-1

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POINCARÉ INEQUALITIES IN WEIGHTED SOBOLEV SPACES

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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 date: 2003-02-25

Revised date: 2005-08-23

Online published: 2006-01-18

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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

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WANG Wan-yi;SUN Jiong;ZHENG Zhi-ming . POINCARÉ INEQUALITIES IN WEIGHTED SOBOLEV SPACES[J]. Applied Mathematics and Mechanics, 2006 , 27(1) : 125 -132 . DOI: 10.1007/s10483-006-0116-1

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