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    Anestopoulos, C. N. and Argyropoulos, E. E. 2006. On the low frequency asymptotics for the 2-D electromagnetic transmission problem. The ANZIAM Journal, Vol. 47, Issue. 03, p. 397.

    Athanasiadis, Christodoulos and Stratis, Ioannis G. 2001. A Transmission problem for bi-isotropic media. Applicable Analysis, Vol. 77, Issue. 3-4, p. 195.

    Mitrea, Dorina and Mitrea, Marius 1998. Uniqueness for inverse conductivity and transmission problems in the class of lipschitz domains. Communications in Partial Differential Equations, Vol. 23, Issue. 7-8, p. 1419.

    Hettlich, F. 1996. Uniqueness of the Inverse Conductive Scattering Problem for Time-Harmonic Electromagnetic Waves. SIAM Journal on Applied Mathematics, Vol. 56, Issue. 2, p. 588.

    Torres, Rodolfo H. 1996. A Transmission Problem in the Scattering of Electromagnetic Waves by a Penetrable Object. SIAM Journal on Mathematical Analysis, Vol. 27, Issue. 5, p. 1406.

    Angell, T. S. and Kirsch, A. 1992. The Conductive Boundary Condition for Maxwell’s Equations. SIAM Journal on Applied Mathematics, Vol. 52, Issue. 6, p. 1597.

    Colton, David and Kirsch, Andreas 1992. The use of polarization effects in electromagnetic inverse scattering problems. Mathematical Methods in the Applied Sciences, Vol. 15, Issue. 1, p. 1.

    Wilde, Peter and Willers, Achim 1988. Dense Sets and Far Field Patterns for the Vector Helmholtz Equation under Transmission Boundary Conditions. SIAM Journal on Mathematical Analysis, Vol. 19, Issue. 2, p. 348.

  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 105, Issue 1
  • January 1987, pp. 61-76

Transmission problems for the vector Helmholtz equation

  • Peter Wilde (a1)
  • DOI:
  • Published online: 14 November 2011

Transmission problems for the vector Helmholtz equation are considered. By using boundary integral equation methods, existence and uniqueness theorems in the form of Fredholm's alternative are established.

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2K. Jörgens . Lineare Integraloperatoren (Stuttgart: Teubner-Verlag, 1970).

4R. Kittappa and R. E. Kleinman . Acoustic scattering by penetrable homogeneous objects. J. Math. Phys. 16 (1975), 421432.

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7W. Knauff and R. Kress . On the exterior boundary-value problem for the time-harmonic Maxwell equations. J. Math. Anal. Appl. 72 (1979), 215235.

8R. Kress . On the Fredholm Alternative. Integral Equations Operator Theory 6 (1983), 453457.

10R. Kress and G. F. Roach . Transmission problems for the Helmholtz equation. J.Math. Phys. 19 (1978), 14331437.

13C. Möller . Grundprobleme der mathematischen Theorie elektromagnetischer Schwingungen (Berlin: Springer, 1957).

14A. G. Ramm . Scattering by a penetrable body. J. Math. Phys. 25 (1984), 469471.

16W. Wendland . Die Fredholmsche Alternative fÜr Operatoren, die bezüglich eines bilinearen Funktionals adjungiert sind. Math. Z. 101 (1967), 6164.

18P. Werner . Zur mathematischen Theorie akustischer Wellenfelder. Arch. Rational Mech. Anal. 6 (1960), 231260.

19P. Werner . Randwertprobleme der mathematischen Akustik. Arch. Rational Mech. Anal. 10 (1962), 2966.

20P. Werner . Beugungsprobleme der mathematischen Akustik. Arch. Rational Mech. Anal. 12 (1963), 155184.

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
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