Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Sharp Integral Inequalities Involving High-Order Partial Derivatives | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 571417 10 pages doi 2008 571417 Research Article Sharp Integral Inequalities Involving High-Order Partial Derivatives Zhao1 and Cheung2 1 Department of Information and Mathematics Sciences College of Science China Jiliang University Hangzhou 310018 China 2 Department of Mathematics The University of Hong Kong Pokfulam Road Hong Kong Correspondence should be addressed to Zhao chjzhao@ Received 28 November 2007 Accepted 10 April 2008 Recommended by Peter Pang 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 Poincare Pachpatte Smith and Stredulinsky s inequalities and provide some new estimates on such types of inequalities. Copyright 2008 Zhao and 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. 1. Introduction Inequalities involving functions of n independent variables their partial derivatives integrals play a fundamental role in establishing the existence and uniqueness of initial and boundary value problems for ordinary and partial differential equations as well as difference equations 1-10 . Especially in view of wider applications inequalities due to Agarwal Opial Pachpatte Wirtinger Poincare and et al. have been generalized and sharpened from the very day of their discover. As a matter of fact these now have become research topic in their own right 11-14 . In the present paper we will use the same method of Agarwal and Sheng 15 establish some new estimates on these types of inequalities involving higher-order partial derivatives. We further generalize these inequalities which lead to result .
