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The Hardy–Rellich inequality for polyharmonic operators

Published online by Cambridge University Press:  14 November 2011

Mark P. Owen
Mark P. Owen
Affiliation:
Department of Mathematics, King's College London, Strand, London WC2R 2LS, UK (mowen@fam.tuwien.ac.at)
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Extract

The Hardy-Rellich inequality given here generalizes a Hardy inequality of Davies, from the case of the Dirichlet Laplacian of a region Ω ⊆ ℝN to that of the higher-order polyharmonic operators with Dirichlet boundary conditions. The inequality yields some immediate spectral information for the polyharmonic operators and also bounds on the trace of the associated semigroups and resolvents.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 129 , Issue 4 , 1999 , pp. 825 - 839
Copyright
Copyright © Royal Society of Edinburgh 1999

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