Extendability of solutions of Helmholtz’s equation to the interior of a two-dimensional scatterer
Authors:
Raul Kangro, Urve Kangro and Roy Nicolaides
Journal:
Quart. Appl. Math. 58 (2000), 591-600
MSC:
Primary 35J05; Secondary 35A30, 35B60
DOI:
https://doi.org/10.1090/qam/1770657
MathSciNet review:
MR1770657
Full-text PDF Free Access
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Additional Information
P. M. van den Berg and J. T. Fokkema, The Rayleigh hypothesis in the theory of reflection by a grating, J. Opt. Soc. Amer. 69, 27–31 (1979)
- Søren Christiansen and Ralph E. Kleinman, On a misconception involving point collocation and the Rayleigh hypothesis, IEEE Trans. Antennas and Propagation 44 (1996), no. 10, 1309–1316. MR 1412211, DOI https://doi.org/10.1109/8.537324
P. Garabedian, Partial Differential Equations, Chelsea Publishing Co., New York, 1967
U. Kangro and R. Nicolaides (to appear)
- Robert F. Millar, Singularities and the Rayleigh hypothesis for solutions to the Helmholtz equation, IMA J. Appl. Math. 37 (1986), no. 2, 155–171. MR 983524, DOI https://doi.org/10.1093/imamat/37.2.155
- C. B. Morrey Jr. and L. Nirenberg, On the analyticity of the solutions of linear elliptic systems of partial differential equations, Comm. Pure Appl. Math. 10 (1957), 271–290. MR 89334, DOI https://doi.org/10.1002/cpa.3160100204
M. Ochmann, The source simulation technique for acoustic radiation problems, Acustica 81, 512–527 (1995)
Lord Rayleigh, On the dynamical theory of gratings, Proc. Roy. Soc. London 79, 399–416 (1907)
P. M. van den Berg and J. T. Fokkema, The Rayleigh hypothesis in the theory of reflection by a grating, J. Opt. Soc. Amer. 69, 27–31 (1979)
S. Christiansen and R. Kleinman, On a misconception involving point collocation and the Rayleigh hypothesis, IEEE Transactions on Antennas and Propagation 44, 1309–1316 (1996)
P. Garabedian, Partial Differential Equations, Chelsea Publishing Co., New York, 1967
U. Kangro and R. Nicolaides (to appear)
R. F. Millar, Singularities and the Rayleigh hypothesis for solutions to the Helmholtz equation, IMA Journal of Applied Mathematics 37, 155–171 (1986)
C. Morrey and L. Nirenberg, On the analyticity of the solutions of linear elliptic systems of partial differential equations, Comm. Pure Appl. Math. 10, 271–290 (1957)
M. Ochmann, The source simulation technique for acoustic radiation problems, Acustica 81, 512–527 (1995)
Lord Rayleigh, On the dynamical theory of gratings, Proc. Roy. Soc. London 79, 399–416 (1907)
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Article copyright:
© Copyright 2000
American Mathematical Society
