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Optimal Hardy-Rellich inequalities, maximum principle and related eigenvalue problem |
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| Authors: | Adimurthi Massimo Grossi |
| Affiliation: | a TIFR Centre, PB 1234, Indian Institute of Science Campus, Bangalore 560 012, India b Universitá degli Studi di Roma “La Sapienza”, Piazzale Aldo Moro, 2, 00185 Roma, Italy c Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India |
| 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  under various assumptions on the perturbation q. |
| Keywords: | Biharmonic equation Hardy-Rellich's inequality Maximum principle Perturbed eigenvalue problem Boggio's principle Dirichlet and Navier boundary conditions |
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