Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 241759, 11 pages
doi:10.1155/2010/241759
Research Article

Poincaré Inequalities with Luxemburg Norms in Lφ(m)-Averaging Domains

Yuming Xing

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received 28 November 2009; Accepted 29 January 2010

Academic Editor: Shusen Ding

Copyright © 2010 Yuming Xing. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove both local and global Poincaré inequalities with Luxemburg norms for differential forms in Lφ(m)-averaging domains, which can be considered as generalizations of the existing versions of Poincaré inequalities.