The exterior Calderón operator for non-spherical objects

Gerhard Kristensson; Ioannis Stratis; Niklas Wellander; Athanasios Yannacopoulos

doi:10.1007/s42985-019-0005-x

The exterior Calderón operator for non-spherical objects

Gerhard Kristensson, Ioannis Stratis, Niklas Wellander, Athanasios Yannacopoulos

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Number of pages	32
Journal	SN Partial Differential Equations and Applications
Volume	1
Issue number	6
DOIs	https://doi.org/10.1007/s42985-019-0005-x
Publication status	Published - 2020

Subject classification (UKÄ)

Mathematical Analysis

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10.1007/s42985-019-0005-xLicence: CC BY

Cite this

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title = "The exterior Calder{\'o}n operator for non-spherical objects",

abstract = "This paper deals with the exterior Calder{\'o}n operator for not necessarily spherical domains. We present a new approach of finding the norm of the exterior Calder{\'o}n 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 Calder{\'o}n operator. The connection of the exterior Calder{\'o}n operator to the transition matrix for a perfectly conducting surface is analyzed.",

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AU - Kristensson, Gerhard

AU - Stratis, Ioannis

AU - Wellander, Niklas

AU - Yannacopoulos, Athanasios

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/85095336237

U2 - 10.1007/s42985-019-0005-x

DO - 10.1007/s42985-019-0005-x

M3 - Article

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VL - 1

JO - SN Partial Differential Equations and Applications

JF - SN Partial Differential Equations and Applications

IS - 6

ER -

The exterior Calderón operator for non-spherical objects

Abstract

Subject classification (UKÄ)

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