×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bachman, G; Narici, L, Functional analysis, (1966), 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] {\scR. F. Goodrich}, private communication, (1974).
[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 New York
[6] Kantorovich, L.V; Akilov, G.P, Functional analysis in normed spaces, (1964), Macmillan New York · Zbl 0127.06104
[7] Kellogg, O.D, Foundations of potential theory, (1929), 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 Toronto
[11] Tikhonov, A.N; Samarskii, A.A, Equations of mathematical physics, (1963), Pergamon Press New York · Zbl 0111.29008
[12] Ursell, F, On the exterior problems of acoustics, (), 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.