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A uniqueness theorem for the Helmholtz' equation: Penetrable media with an infinite interface

Kristensson, Gerhard LU (1980) In SIAM Journal on Mathematical Analysis 11(6). p.1104-1117
Abstract
In this paper we will prove the uniqueness of a solution to Helmholtz' equation for two halfspaces of different media in $n$ dimensions. The theorem allows a finite number of bounded inhomogeneities in each half space. The surface separating the half spaces is assumed to be a cone of arbitrary cross section far away from the origin and is furthermore assumed to be smooth. We assume all space to be lossless, and in each halfspace we assume a radiation condition to be fulfilled. The boundary conditions at the interface are a general coupling in the field and its normal derivative with constant coefficients.
Please use this url to cite or link to this publication:
author
publishing date
type
Contribution to journal
publication status
published
subject
in
SIAM Journal on Mathematical Analysis
volume
11
issue
6
pages
1104 - 1117
publisher
Society for Industrial and Applied Mathematics
ISSN
0036-1410
DOI
10.1137/0511096
language
English
LU publication?
no
id
da679302-2949-413c-a66c-104caae8a4d8 (old id 1041179)
date added to LUP
2016-04-04 09:43:55
date last changed
2020-02-26 15:00:53
@article{da679302-2949-413c-a66c-104caae8a4d8,
  abstract     = {{In this paper we will prove the uniqueness of a solution to Helmholtz' equation for two halfspaces of different media in $n$ dimensions. The theorem allows a finite number of bounded inhomogeneities in each half space. The surface separating the half spaces is assumed to be a cone of arbitrary cross section far away from the origin and is furthermore assumed to be smooth. We assume all space to be lossless, and in each halfspace we assume a radiation condition to be fulfilled. The boundary conditions at the interface are a general coupling in the field and its normal derivative with constant coefficients.}},
  author       = {{Kristensson, Gerhard}},
  issn         = {{0036-1410}},
  language     = {{eng}},
  number       = {{6}},
  pages        = {{1104--1117}},
  publisher    = {{Society for Industrial and Applied Mathematics}},
  series       = {{SIAM Journal on Mathematical Analysis}},
  title        = {{A uniqueness theorem for the Helmholtz' equation: Penetrable media with an infinite interface}},
  url          = {{http://dx.doi.org/10.1137/0511096}},
  doi          = {{10.1137/0511096}},
  volume       = {{11}},
  year         = {{1980}},
}