On Opial-type inequalities with higher order partial derivatives

摘要

In the present paper we establish some new Opial-type inequalities involving higher order partial derivatives. Our results in special cases yield some of the recent results on Opial's inequality and provide new estimates on inequalities of this type. As an application, we prove the uniqueness of the solution of the initial value problem involving higher order partial differential equations. © 2012 Elsevier Ltd. All rights reserved.