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 |
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Related URLs: | |

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.ernet.in/id/eprint/14072 |

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