The exterior Calderón operator for non-spherical objects

Gerhard Kristensson (), Ioannis G. Stratis (), Niklas Wellander () and Athanasios N. Yannacopoulos ()
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Gerhard Kristensson: Lund University
Ioannis G. Stratis: National and Kapodistrian University of Athens
Niklas Wellander: Swedish Defense Research Agency, FOI
Athanasios N. Yannacopoulos: Athens University of Economics and Business

Partial Differential Equations and Applications, 2020, vol. 1, issue 1, 1-32

Abstract: 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.

Keywords: 35B65; 35Q61; 35R01; 45A05; 45P05 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s42985-019-0005-x

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