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Kress, Rainer

On the limiting behaviour of solutions to boundary integral equations associated with time harmonic wave equations for small frequencies. (English) Zbl 0418.35031

Math. Methods Appl. Sci. 1, 89-100 (1979).
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Cited in 2 Reviews
Cited in 18 Documents

MSC:

35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J10 Schrödinger operator, Schrödinger equation
35B25 Singular perturbations in context of PDEs
45B05 Fredholm integral equations

Keywords:

boundary value problems; Helmholtz equation; Maxwell equation; boundary integral equations; compact linear operators; transmission problem
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\textit{R. Kress}, Math. Methods Appl. Sci. 1, 89--100 (1979; Zbl 0418.35031)
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References:

[1] Jörgens, Lineare Integraloperatoren (1970)
[2] MacCamey, Low frequency acoustic oscillations, Quart. Appl. Math. 23 pp 247– (1965)
[3] Martensen, Potentialtheorie (1968)
[4] Martensen, Vektorielle Differentialgleichungsprobleme der Potentialtheorie, Z. f. angew. Math. Mech. 52 pp T17– (1972)
[5] Müller, Grundprobleme der mathematischen Theorie elektromagnetischer Schwingungen (1957) · Zbl 0087.21305
[6] Leis, Vorlesungen über partielle Differentialgleichungen zweiter Ordnung (1967)
[7] Kress, Ein Iterationsverfahren für eine Klasse von Funktionalgleichungen zweiter Art, J. f. d. reine u. angew. Math. 238 pp 207– (1969) · Zbl 0177.19702
[8] Kress, Grundzüge einer Theorie der verallgemeinerten harmonischen Vektorfelder, Meth. Verf. Math. Phys. 2 pp 49– (1969) · Zbl 0195.11503
[9] Kress, Die Behandlung zweier Randwertprobleme für die vektorielle Poissongleichung nach einer Integralgleichungsmethode, Arch. Rat. Mech. Anal. 39 pp 206– (1970) · Zbl 0208.36902
[10] Steffen , R. Behandlung von elektro- und magnetostatischen Übergangsproblemen nach der Integralgleichungsmethode 1978
[11] Wendland, Bemerkungen über die Fredholmschen Sätze, Meth. Verf. Math. Phys. 3 pp 141– (1970)
[12] Werner, On the exterior boundary value problem of perfect reflection for stationary electromagnetic wave fields, J. Math. Anal. Appl. 7 pp 348– (1963) · Zbl 0118.43501
[13] Werner, On an integral equation in electromagnetic diffraction theory, J. Math. Anal. Appl. 14 pp 445– (1966) · Zbl 0151.43102
[14] Werner, On the behaviour of stationary electromagnetic wave fields for small frequencies, J. Math. Anal. Appl. 15 pp 447– (1966)
[15] Werner, Über das Verhalten elektromagnetischer Felder für kleine Frequenzen in mehrfach zusammenhängenden Gebieten, J. f. d. reine angew. Math. I 278/279 pp 365– (1975) · Zbl 0312.35062
[16] J. f. d. reine angew. Math. I II pp 280– (1976)
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