Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 571417, 10 pages
Sharp Integral Inequalities Involving High-Order Partial Derivatives
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.