The Calderón approach to an elliptic boundary problem

✍ Scribed by M. Faierman

• Publisher: John Wiley and Sons
• Year: 2009
• Tongue: English
• Weight: 337 KB
• Volume: 282
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200610792

✦ Synopsis

Abstract

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 of 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 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)