GENERALIZED HARDY–RELLICH INEQUALITIES IN CRITICAL DIMENSION AND ITS APPLICATIONS

Abstract

In this paper, we study the Hardy–Rellich inequalities for polyharmonic operators in the critical dimension and an analogue in the p-biharmonic case. We also develop some optimal weighted Hardy–Sobolev inequalities in the general case and discuss the related eigenvalue problem. We also prove W 2,q (Ω) estimates in the biharmonic case.