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The exterior Calderón operator for non-spherical objects

Kristensson, Gerhard LU ; Stratis, Ioannis ; Wellander, Niklas and Yannacopoulos, Athanasios (2020) In SN Partial Differential Equations and Applications 1(6).
Abstract
This paper deals with the exterior Calderón operator for not necessarily spherical domains. We present a new approach of finding the norm of the exterior Calderón operator for a wide class of surfaces. The basic tool in the treatment is the set of eigenfunctions and eigenvalues to the Laplace–Beltrami operator for the surface. The norm is obtained in view of an eigenvalue problem of a quadratic form containing the exterior Calderón operator. The connection of the exterior Calderón operator to the transition matrix for a perfectly conducting surface is analyzed.
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author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
SN Partial Differential Equations and Applications
volume
1
issue
6
pages
32 pages
publisher
Springer
ISSN
2662-2963
DOI
10.1007/s42985-019-0005-x
language
English
LU publication?
yes
id
cbd295e5-ede4-4541-9b6c-0388a71e411b
date added to LUP
2018-03-26 15:54:21
date last changed
2020-02-04 10:14:16
@article{cbd295e5-ede4-4541-9b6c-0388a71e411b,
  abstract     = {This paper deals with the exterior Calderón operator for not necessarily spherical domains. We present a new approach of finding the norm of the exterior Calderón operator for a wide class of surfaces. The basic tool in the treatment is the set of eigenfunctions and eigenvalues to the Laplace–Beltrami operator for the surface. The norm is obtained in view of an eigenvalue problem of a quadratic form containing the exterior Calderón operator. The connection of the exterior Calderón operator to the transition matrix for a perfectly conducting surface is analyzed.},
  author       = {Kristensson, Gerhard and Stratis, Ioannis and Wellander, Niklas and Yannacopoulos, Athanasios},
  issn         = {2662-2963},
  language     = {eng},
  number       = {6},
  publisher    = {Springer},
  series       = {SN Partial Differential Equations and Applications},
  title        = {The exterior Calderón operator for non-spherical objects},
  url          = {http://dx.doi.org/10.1007/s42985-019-0005-x},
  doi          = {10.1007/s42985-019-0005-x},
  volume       = {1},
  year         = {2020},
}