On the complex spectra of second order elliptic systems
type: Item
instance of: scholarly article
title: On the complex spectra of second order elliptic systems
zbMATH Open document ID: 0681.35065
DOI: 10.1007/BF03322444
published in: Results in Mathematics
publication date: 1989-01-01T00:00:00Z
review text: The author studies the complex spectra of second order elliptic systems \[ Lu\equiv -A_{ij}(x)u_{,ij}+B_ i(x),u_{,i}+C(x)u=\lambda M(x)u\quad in\quad \Omega,\quad u=0\quad on\quad \partial \Omega, \] \(\Omega \subset {\mathbb{R}}^ n\) a bounded \(C^{2+\theta}\)-domain, \(A_{ij}\), \(B_ i\), C, M are \(N\times N\)-matrices, \(A_{ij}\) satisfies \(Re a^{\alpha \beta}_{ij}(x) \xi^{\alpha}_ i {\bar \xi}^{\beta}_ j\geq a_ 0| \xi /^ 2\) (for some \(a_ 0>0)\) for all \(\xi \in {\mathbb{C}}^{nN}\), \(x\in {\bar \Omega}\); \(\lambda\in {\mathbb{C}}\) is the eigenvalue parameter. Under various conditions on L and M bounds are given for the real parts of the eigenvalues. The first part is based on integration by parts and the second one on the maximum principle for elliptic equations (with stronger structure conditions). This paper gives an extensive discussion of related results for elliptic equations.
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 35J55
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 4115153
zbMATH Keywords: stability
zbMATH Keywords: integration by parts
zbMATH Keywords: maximum principle
author: Chris Cosner
reviewed by: Reinhard Racke
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4115153