Journal of Inequalities and Applications 
Volume 2008 (2008), Article ID 571417, 10 pages
doi:10.1155/2008/571417
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

Recommended by Peter Pang

Abstract

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.