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Spectral theory of elliptic differential operators with indefinite weights

Published online by Cambridge University Press:  30 January 2013

Jussi Behrndt
Jussi Behrndt*
Affiliation:
Institut für Numerische Mathematik, Technische Universität Graz, Steyrergasse 30, 8010 Graz, Austria ([email protected])
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Abstract

The spectral properties of a class of non-self-adjoint second-order elliptic operators with indefinite weight functions on unbounded domains Ω are investigated. It is shown, under an abstract regularity assumption, that the non-real spectrum of the associated elliptic operators in L2(Ω) is bounded. In the special case where Ω = ℝn decomposes into subdomains Ω+ and Ω− with smooth compact boundaries and the weight function is positive on Ω+ and negative on Ω−, it turns out that the non-real spectrum consists only of normal eigenvalues that can be characterized with a Dirichlet-to-Neumann map.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 143 , Issue 1 , February 2013 , pp. 21 - 38
Copyright
Copyright © Royal Society of Edinburgh 2013

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