×

The exterior Dirichlet problem for the Helmholtz equation. (English) Zbl 0326.45001


MSC:

45B05 Fredholm integral equations
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bachman, G.; Narici, L., Functional Analysis (1966), Academic Press: Academic Press New York · Zbl 0141.11502
[2] Brakhage, H.; Werner, P., Über das Dirichletsche Aussenraumproblem für die Helmholtzsche Schwingungsgleichung, Arch. Math., 16, 325-329 (1965) · Zbl 0132.33601
[3] R. F. Goodrich; R. F. Goodrich
[4] Greenspan, D.; Werner, P., A numerical method for the exterior Dirichlet problem for the reduced wave equation, Arch. Rational Mech. Anal., 23, 288-316 (1966) · Zbl 0161.12701
[5] Haack, W.; Wendland, W., Lectures on Partial and Pfaffian Differential Equations (1972), Pergamon Press: Pergamon Press New York
[6] Kantorovich, L. V.; Akilov, G. P., Functional Analysis in Normed Spaces (1964), Macmillan: Macmillan New York · Zbl 0127.06104
[7] Kellogg, O. D., Foundations of Potential Theory (1929), Springer: Springer Berlin · Zbl 0152.31301
[8] Kleinman, R. E., The Dirichlet problem for the Helmholtz equation, Arch. Rational Mech. Anal., 18, 205-229 (1965) · Zbl 0132.33701
[9] Kleinman, R. E.; Roach, G. F., Boundary integral equations for the three-dimensional Helmholtz equation, SIAM Rev., 16, 214-236 (1974) · Zbl 0253.35023
[10] Sternberg, W. J.; Smith, T. L., The Theory of Potential and Spherical Harmonics (1946), University of Toronto Press: University of Toronto Press Toronto
[11] Tikhonov, A. N.; Samarskii, A. A., Equations of Mathematical Physics (1963), Pergamon Press: Pergamon Press New York · Zbl 0111.29008
[12] Ursell, F., On the exterior problems of acoustics, (Proc. Cambridge Philos. Soc., 74 (1973)), 117-125 · Zbl 0259.35019
[13] Weyl, H., Kapazität von Strahlungsfeldern, Math. Z., 55, 187-198 (1952) · Zbl 0046.10706
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.