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References
Atkinson, K., Han, W.: Theoretical Numerical Analysis: A Functional Analysis Framework. Springer, New York (2001).
Chen, G., Zhou, J.: Boundary Element Methods. Academic Press, London (1992).
Colton, D.L., Kress, R.: Integral Equation Methods in Scattering Theory. Wiley, New York (1983).
Costabel, M., Stephan, E.: A direct boundary integral equation method for transmission problems. J. Math. Anal. Appl., 106, 367–413 (1985).
Domínguez, V., Rapún, M.–L., Sayas, F.–J.: Dirac delta methods for Helmholtz transmission problems. Adv. Comput. Math. (in press).
Kleinman, R.E., Martin, P.A.: On single integral equations for the transmission problem of acoustics. SIAM J. Appl. Math., 48, 307–325 (1988).
Kress, R., Roach, G.F.: Transmission problems for the Helmholtz equation. J. Math. Phys., 19, 1433–1437 (1978).
Mandelis, A.: Diffusion–Wave Fields. Mathematical Methods and Green Functions. Springer, New York (2001).
McLean, W.: Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press, Cambridge (2000).
Rapún, M.-L., Sayas, F.-J.: Boundary integral approximation of a heat diffusion problem in time-harmonic regime. Numer. Algorithms, 41, 127–160 (2006).
Rapún, M.-L., Sayas, F.-J.: Indirect methods with Brakhage–Werner potentials for Helmholtz transmission problems. In: Proceedings of ENUMATH 2005. Springer, New York (2006), pp. 1146–1154.
Terrón, J.M., Salazar, A., Sánchez–Lavega, A.: General solution for the thermal wave scattering in fiber composites. J. Appl. Phys., 91, 1087–1098 (2002).
Torres, R.H., Welland, G.V.: The Helmholtz equation and transmission problems with Lipschitz interfaces. Indiana Univ. Math. J., 42, 1457–1485 (1993).
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Rapún, ML., Sayas, FJ. (2008). Exterior Dirichlet and Neumann Problems for the Helmholtz Equation as Limits of Transmission Problems. In: Constanda, C., Potapenko, S. (eds) Integral Methods in Science and Engineering. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4671-4_24
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