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Spectral analysis for optical fibres and stratified fluids. I: The limiting absorption principle. (English) Zbl 0731.35069
The authors prove a limiting absorption principle for the operator \[ H=- c^ 2(z)\rho (z)\nabla_ z\cdot \rho^{-1}(z)\nabla_ z \] on \({\mathbb{R}}^ n\). The functions \(\rho\) and c are supposed to satisfy many very precise assumptions concerning their regularity and their behaviour at infinity. The proof is based on Mourre theory, and the main step consists in proving a Mourre estimate on H.

MSC:
35P05 General topics in linear spectral theory for PDEs
35J20 Variational methods for second-order elliptic equations
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