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

• Articles • Previous Articles     Next Articles

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

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

2010 MSC Number: 

APS Journals | CSTAM Journals | AMS Journals | EMS Journals | ASME Journals