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

Adimurthi, * and Grossi, Massimo and Santra, Sanjiban (2006) Optimal Hardy–Rellich inequalities, maximum principle and related eigenvalue problem. In: Journal of Functional Analysis, 240 (1). pp. 36-83.

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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 ${ \Delta}^2 $ = $\frac {n^2(n-4)^2}{16}$ $ \frac {q(x)}{ |x|^4}$ under various assumptions on the perturbation q.

Item Type:	Journal Article
Publication:	Journal of Functional Analysis
Publisher:	Elsevier Science
Additional Information:	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;
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	28 May 2008
Last Modified:	01 Mar 2012 08:51
URI:	http://eprints.iisc.ac.in/id/eprint/14072

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