The exterior Calderón operator for non-spherical objects

Gerhard Kristensson; Ioannis Stratis; Niklas Wellander; Athanasios Yannacopoulos

The exterior Calderón operator for non-spherical objects

Gerhard Kristensson, Ioannis Stratis, Niklas Wellander, Athanasios Yannacopoulos

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Abstract

This paper deals with the exterior Calderón operator for Lipschitz surfaces. We present a new approach of nding the norm of the exterior Calderón operator for this class of surfaces. The basic tool in the treatment is the set of eigenfunctions and eigenvalues of the Laplace-Beltrami operator for the surface. The norm is obtained as an eigenvalue problem of a quadratic form containing the exterior Calderón operator. The connection of the exterior Calderón to the transition matrix for a perfectly conducting surface is analyzed.

Original language	English
Publisher	The Department of Electrical and Information Technology
Number of pages	43
Volume	TEAT-7259
Publication status	Published - 2017

Publication series

Name	Technical Report LUTEDX/(TEAT-7259)/1-41/(2017)
Volume	TEAT-7259

Subject classification (UKÄ)

Other Electrical Engineering, Electronic Engineering, Information Engineering

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TEAT-7259-rev1Final published version, 671 KB

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The exterior Calderón operator for non-spherical objects
Kristensson, G., Stratis, I., Wellander, N. & Yannacopoulos, A., 2020, In: SN Partial Differential Equations and Applications. 1, 6, 32 p.
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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 Lipschitz surfaces. We present a new approach of nding the norm of the exterior Calder{\'o}n operator for this class of surfaces. The basic tool in the treatment is the set of eigenfunctions and eigenvalues of the Laplace-Beltrami operator for the surface. The norm is obtained as an eigenvalue problem of a quadratic form containing the exterior Calder{\'o}n operator. The connection of the exterior Calder{\'o}n to the transition matrix for a perfectly conducting surface is analyzed.",

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AU - Stratis, Ioannis

AU - Wellander, Niklas

AU - Yannacopoulos, Athanasios

PY - 2017

Y1 - 2017

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AB - This paper deals with the exterior Calderón operator for Lipschitz surfaces. We present a new approach of nding the norm of the exterior Calderón operator for this class of surfaces. The basic tool in the treatment is the set of eigenfunctions and eigenvalues of the Laplace-Beltrami operator for the surface. The norm is obtained as an eigenvalue problem of a quadratic form containing the exterior Calderón operator. The connection of the exterior Calderón to the transition matrix for a perfectly conducting surface is analyzed.

M3 - Report

VL - TEAT-7259

T3 - Technical Report LUTEDX/(TEAT-7259)/1-41/(2017)

BT - The exterior Calderón operator for non-spherical objects

PB - The Department of Electrical and Information Technology

ER -

The exterior Calderón operator for non-spherical objects

Abstract

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The exterior Calderón operator for non-spherical objects

Cite this