The Calderón approach to an elliptic boundary problem |
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Authors: | M. Faierman |
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Affiliation: | School of Mathematics and Statistics, The University of New South Wales, UNSWSydney, NSW 2052, Australia |
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Abstract: | We consider a boundary problem for an elliptic system in a bounded region Ω ? ?n and where the spectral parameter is multiplied by a discontinuous weight function ω (x) = diag(ω1(x), …, ωN (x)). The problem is considered under limited smoothness assumptions and under an ellipticity with parameter condition. Recently, this problem was studied under the assumption that the ωj (x)–1 are essentially bounded in Ω. In this paper we suppose that ω (x) vanishes identically in a proper subregion Ω of Ω and that the ωj (x)–1 are essentially bounded in . Then by using methods which are a variant of those used in constructing the Calderón projectors for the boundary Γ of Ω, we shall derive results here which will enable us in a subsequent work to apply the ideas of Calderón to develop the spectral theory associated with the problem under consideration here (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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Keywords: | Elliptic system weight function vanishes identically Calderó n projectors spectral theory |
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