Optimal Hardy-Rellich inequalities, maximum principle and related eigenvalue problem

Adimurthi, ; Grossi, Massimo ; Santra, Sanjiban (2006) Optimal Hardy-Rellich inequalities, maximum principle and related eigenvalue problem Journal of Functional Analysis, 240 (1). pp. 36-83. ISSN 0022-1236

[img]
Preview
PDF - Publisher Version
358kB

Official URL: http://dx.doi.org/10.1016/j.jfa.2006.07.011

Related URL: http://dx.doi.org/10.1016/j.jfa.2006.07.011

Abstract

In this paper we deal with three types of problems concerning the Hardy-Rellich's embedding for a bi-Laplacian operator. First we obtain the Hardy-Rellich inequalities in the critical dimension n=4. Then we derive a maximum principle for fourth order operators with singular terms. Then we study the existence, non-existence, simplicity and asymptotic behavior of the first eigenvalue of the Hardy-Rellich operator Δ2-n2(n-4)2/16 q(x)/|x|4 under various assumptions on the perturbation q.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Biharmonic Equation; Hardy-rellich's Inequality; Maximum Principle; Perturbed Eigenvalue Problem; Boggio's Principle; Dirichlet and Navier Boundary Conditions
ID Code:11893
Deposited On:13 Nov 2010 13:39
Last Modified:16 May 2016 21:18

Repository Staff Only: item control page