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Existence of outgoing solutions for perturbations of and applications to the scattering matrix

Published online by Cambridge University Press:  24 October 2008

Kazuhiro Yamamoto
Kazuhiro Yamamoto
Affiliation:
Department of Mathematics, Nagoya Institute of Technology, Nagoya, Gokiso-cho, 466, Japan
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Extract

In this paper we shall prove an existence theorem and give applications of an outgoing solution of the following problem:

where L(x, x) is a second order elliptic differential operator with a potential term q(x), is an exterior domain of ℝn (where n 2) with the C2-class boundary , k is an element of the complex plane or of a logarithmic Riemann surface, and B is either a Dirichlet boundary condition or of the form Bu = vj(x) ajk(x) ku + (x)u with the unit outer normal vector v(x) = (vl,, vn) at x.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 111 , Issue 2 , March 1992 , pp. 399 - 415
Copyright
Copyright © Cambridge Philosophical Society 1992

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