On Some Variational Inequalities Involving Second-Order Partial Derivatives

Some sharp integral inequalities involving partial derivatives

* Correspondence: chjzhao@163. com Department of Mathematics, China Jiliang University, Hangzhou 310018, P. R. China Full list of author information is available at the end of the article Abstract The main purpose of the present article is to establish some new sharp integral inequalities in 2n independent variables. Our results in special cases yield some of the recent results on Pachpatter, A...

Sharp Integral Inequalities Involving High-Order Partial Derivatives

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, Poi...

Some Opial Dynamic Inequalities Involving Higher Order Derivatives on Time Scales

A Variational Method for Second Order Shape Derivatives

We consider shape functionals obtained as minima on Sobolev spaces of classical integrals having smooth and convex densities, under mixed Dirichlet-Neumann boundary conditions. We propose a new approach for the computation of the second order shape derivative of such functionals, yielding a general existence and representation theorem. In particular, we consider the p-torsional rigidity functio...

Solving Variational Inequalities Involving Nonexpansive Type Mappings

The purpose of this paper is to investigate the asymptotic behavior of algorithms for finding solutions for a certain class of variational inequalities V ID(C, I−f) involving nonexpansive type mappings in smooth Banach spaces. We study existence of solutions of variational inequalities V ID(C, I− f) when D is the set of solutions of zeros of accretive operators or the set of fixed points of non...