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Sharp boundary estimates for elliptic operators

Published online by Cambridge University Press:  01 July 2000

E. B. DAVIES
E. B. DAVIES
Affiliation:
Department of Mathematics, King's College, Strand, London WC2R 2LS; e-mail: [email protected]
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Abstract

We prove sharp L2 boundary decay estimates for the eigenfunctions of certain second order elliptic operators acting in a bounded region, and of their first space derivatives, using only the Hardy inequality. These imply L2 boundary decay properties of the heat kernel and spectral density. We deduce bounds on the rate of convergence of the eigenvalues when the region is slightly reduced in size. It is remarkable that several of the bounds do not involve the space dimension.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 129 , Issue 1 , July 2000 , pp. 165 - 178
Copyright
2000 Cambridge Philosophical Society

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