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Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Seriya Matematika, Mekhanika, Informatika, 2012, Volume 12, Issue 1, Pages 102–113 (Mi vngu111)  

Reflection principle for solutions of the Helmholtz equation in a half-space

V. I. Kuzovatov, A. M. Kytmanov

Institute of Mathematics, Siberian Federal University, Krasnoyarsk, Russia
References:
Abstract: In this paper we consider the reflection principle for functions satisfying the Helmholtz equation in a half-space. The idea of a proof is to perform continuation of a solution of the Helmholtz equation from an upper half-space into the entire space. It is obtained an analog of Liuvill' theorem. This result states that the function which satisfies the Helmholtz equation (with negative parameter) in the upper half-space, which grows not faster than the power function in the upper half-space and which is equal to zero on a hyperplane is identically equal to zero in the entire space.
Keywords: reflection principle, Helmholtz equation, a half-space.
Received: 17.12.2010
English version:
Journal of Mathematical Sciences, 2014, Volume 198, Issue 5, Pages 564–574
DOI: https://doi.org/10.1007/s10958-014-1808-0
Document Type: Article
UDC: 517.95
Language: Russian
Citation: V. I. Kuzovatov, A. M. Kytmanov, “Reflection principle for solutions of the Helmholtz equation in a half-space”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 12:1 (2012), 102–113; J. Math. Sci., 198:5 (2014), 564–574
Citation in format AMSBIB
\Bibitem{KuzKyt12}
\by V.~I.~Kuzovatov, A.~M.~Kytmanov
\paper Reflection principle for solutions of the Helmholtz equation in a~half-space
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2012
\vol 12
\issue 1
\pages 102--113
\mathnet{http://mi.mathnet.ru/vngu111}
\transl
\jour J. Math. Sci.
\yr 2014
\vol 198
\issue 5
\pages 564--574
\crossref{https://doi.org/10.1007/s10958-014-1808-0}
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    Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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    References:83
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