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The exterior Neumann problem for the three-dimensional Helmholtz equation. (English) Zbl 0149.31804


MSC:

35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J40 Boundary value problems for higher-order elliptic equations
35C10 Series solutions to PDEs

Citations:

Zbl 0132.33701
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Full Text: DOI

References:

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[5] Kellogg, O.D. Foundations of Potential Theory. Berlin: Springer 1929. · JFM 55.0282.01
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[8] Meixner, J., Die Kantenbedingung in der Theorie der Beugung elektromagnetischer Wellen an vollkommen leitenden ebenen Schirmen. Ann. Phys. 6, 2–9 (1949). · Zbl 0034.12501
[9] Müller, C., Zur Methode der Strahlungskapazität von H. Weyl. Math. Z. 56, 80–83 (1952). · Zbl 0046.10705 · doi:10.1007/BF01215039
[10] Noble, B., Integral Equation Perturbation Methods in Low Frequency Diffraction. From: Electromagnetic Waves (R. Langer, ed.). Madison: The University of Wisconsin Press 1962.
[11] Sommerfeld, A., Die Greensche Funktion der Schwingungsgleichung. Jahresber. Math.-Verein, 21, 309–353 (1912). · JFM 43.0819.01
[12] Sommerfeld, A., Partial Differential Equations in Physics. New York: Academic Press 1949. · Zbl 0034.35702
[13] Werner, P., Randwertprobleme der mathematischen Akustik. Arch. Rational Mech. Anal. 10, 29–66 (1962). · Zbl 0105.07405 · doi:10.1007/BF00281177
[14] Weyl, H., Kapazität von Strahlungsfeldern. Math. Z. 55, 187–198 (1952). · Zbl 0046.10706 · doi:10.1007/BF01268654
[15] Wilcox, C.H., A generalization of theorems of Rellich and Atkinson. Proc. Amer. Math. Soc. 7, 271–276 (1956). · Zbl 0074.08102 · doi:10.1090/S0002-9939-1956-0078912-4
[16] Wilcox, C.H., Spherical means and radiation conditions. Arch. Rational Mech. Anal. 3, 133–148 (1959). · Zbl 0087.09603 · doi:10.1007/BF00284171
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