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The Calderón approach to an elliptic boundary problem
Author(s) -
Faierman M.
Publication year - 2009
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200610792
Subject(s) - bounded function , mathematics , smoothness , boundary (topology) , function (biology) , boundary value problem , mathematical analysis , boundary problem , work (physics) , pure mathematics , physics , thermodynamics , evolutionary biology , biology
We consider a boundary problem for an elliptic system in a bounded region Ω ⊂ ℝ n and where the spectral parameter is multiplied by a discontinuous weight function ω ( x ) = diag( ω 1 ( x ), …, ω N ( 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 ω j ( x ) –1 are essentially bounded in Ω. In this paper we suppose that ω ( x ) vanishes identically in a proper subregion Ω N 0of Ω and that the ω j ( 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 N 0of Ω N 0, 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)