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Eigenvalue asymptotics for an elliptic boundary problem

Published online by Cambridge University Press:  26 March 2007

M. Faierman  and
M. Möller
M. Faierman
Affiliation:
School of Mathematics, The University of New South Wales, Sydney, NSW 2052, Australia
M. Möller
Affiliation:
The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, Johannesburg, WITS 2050, South Africa (manfred@maths.wits.ac.za)
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Abstract

We consider an elliptic boundary problem in a bounded region Ω ⊂ ℝn wherein the spectral parameter is multiplied by a real-valued weight function with the property that it, together with its reciprocal, is essentially bounded in Ω. The problem is considered under limited smoothness assumptions and under an ellipticity with parameter condition. Then, fixing our attention upon the operator induced on L2(Ω) by the boundary problem under null boundary conditions, we establish results pertaining to the asymptotic behaviour of the eigenvalues of this operator under weaker smoothness assumptions than have hitherto been supposed.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 137 , Issue 2 , 2007 , pp. 281 - 302
Copyright
Copyright © Royal Society of Edinburgh 2007

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