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The exterior Calderón operator for non-spherical objects

Author

Listed:
  • 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)

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.

Suggested Citation

  • Gerhard Kristensson & Ioannis G. Stratis & Niklas Wellander & Athanasios N. Yannacopoulos, 2020. "The exterior Calderón operator for non-spherical objects," Partial Differential Equations and Applications, Springer, vol. 1(1), pages 1-32, February.
    • Handle: RePEc:spr:pardea:v:1:y:2020:i:1:d:10.1007_s42985-019-0005-x
    DOI: 10.1007/s42985-019-0005-x
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    Keywords

    35B65; 35Q61; 35R01; 45A05; 45P05;
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