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The exterior Neumann problem for the three-dimensional Helmholtz equation

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References

  1. Atkinson, F.V., On Sommerfeld's radiation condition. Philos. Mag. 40, Series 7, No. 305. 645–651 (1949).

    Google Scholar 

  2. Barrar, R.B., & A.F. Kay, A Series Development of the Wave Equation in Powers of 1/r, Internal Memorandum Tech. Res. Group, Inc.

  3. Bouwkamp, C.J., Diffraction theory. Rep. Progr. Phys. 17, 35–100 (1954).

    Google Scholar 

  4. Darling, D.A., & T.B.A. Senior, Low frequency expansions for scattering by separable and nonseparable bodies. J. Acoust. Soc. Amer. 37, No. 2, 228–234 (1965).

    Google Scholar 

  5. Kellogg, O.D. Foundations of Potential Theory. Berlin: Springer 1929.

    Google Scholar 

  6. Kleinman, R.E., The Dirichlet problem for the Heimholte equation. Arch. Rational Mech. Anal. 18, 205–229 (1965).

    Google Scholar 

  7. Leis, R., Über das Neumannsche Randwertproblem für die Helmholtzsche Schwingungs-gleichung. Arch. Rational Mech. Anal. 2, 101–113 (1958).

    Google Scholar 

  8. Meixner, J., Die Kantenbedingung in der Theorie der Beugung elektromagnetischer Wellen an vollkommen leitenden ebenen Schirmen. Ann. Phys. 6, 2–9 (1949).

    Google Scholar 

  9. Müller, C., Zur Methode der Strahlungskapazität von H. Weyl. Math. Z. 56, 80–83 (1952).

    Google Scholar 

  10. Noble, B., Integral Equation Perturbation Methods in Low Frequency Diffraction. From: Electromagnetic Waves (R. Langer, ed.). Madison: The University of Wisconsin Press 1962.

    Google Scholar 

  11. Sommerfeld, A., Die Greensche Funktion der Schwingungsgleichung. Jahresber. Math.-Verein, 21, 309–353 (1912).

    Google Scholar 

  12. Sommerfeld, A., Partial Differential Equations in Physics. New York: Academic Press 1949.

    Google Scholar 

  13. Werner, P., Randwertprobleme der mathematischen Akustik. Arch. Rational Mech. Anal. 10, 29–66 (1962).

    Google Scholar 

  14. Weyl, H., Kapazität von Strahlungsfeldern. Math. Z. 55, 187–198 (1952).

    Google Scholar 

  15. Wilcox, C.H., A generalization of theorems of Rellich and Atkinson. Proc. Amer. Math. Soc. 7, 271–276 (1956).

    Google Scholar 

  16. Wilcox, C.H., Spherical means and radiation conditions. Arch. Rational Mech. Anal. 3, 133–148 (1959).

    Google Scholar 

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Authors and Affiliations

  1. Radiation Laboratory, University of Michigan, Ann Arbor

    Ergun Ar & R. E. Kleinman

  2. Laboratory of Electromagnetic Theory, Technical University of Denmark, Lyngby

    Ergun Ar & R. E. Kleinman

Authors
  1. Ergun Ar
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  2. R. E. Kleinman
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Communicated by J. Meixner

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Ar, E., Kleinman, R.E. The exterior Neumann problem for the three-dimensional Helmholtz equation. Arch. Rational Mech. Anal. 23, 218–236 (1966). https://doi.org/10.1007/BF00253158

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  • DOI: https://doi.org/10.1007/BF00253158

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