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An elliptic boundary problem involving a semi-definite weight

Published online by Cambridge University Press:  12 July 2007

M. Faierman
M. Faierman
Affiliation:
School of Mathematics, The University of New South Wales, Sydney, NSW 2052, Australia
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Abstract

We consider an elliptic boundary problem defined in a bounded region Ω ⊂ Rn and where the spectral parameter is multiplied by a weight function ω(x). We suppose that ω(x) ≠ 0 for x ∈ Ω, but vanishes in a specified manner on the boundary of Ω. Under limited smoothness assumptions, we derive results pertaining to existence and uniqueness of and a priori estimates for solutions of the boundary problem. If S(λ) denotes the operator pencil induced in L2(Ω) by the boundary problem with zero boundary conditions, then results are also derived pertaining to the spectral properties of S(λ).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 1 , February 2004 , pp. 109 - 136
Copyright
Copyright © Royal Society of Edinburgh 2004

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