Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 571417, 10 pages
Research Article

Sharp Integral Inequalities Involving High-Order Partial Derivatives

C.-J Zhao1 and W.-S Cheung2

1Department of Information and Mathematics Sciences, College of Science, China Jiliang University, Hangzhou 310018, China
2Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong

Received 28 November 2007; Accepted 10 April 2008

Academic Editor: Peter Pang

Copyright © 2008 C.-J Zhao and W.-S Cheung. 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.


The main purpose of the present paper is to establish some new sharp integral inequalities involving higher-order partial derivatives. Our results in special cases yield some of the recent results on Agarwal, Wirtinger, Poincaré, Pachpatte, Smith, and Stredulinsky's inequalities and provide some new estimates on such types of inequalities.