Symmetry Principle for Solutions of the Helmholtz Equation in a Half-Space

We establish the symmetry principle for solutions to the Helmholtz equation in a halfspace. The proof is based on the extension of the solution from the upper half-space to the entire space. An analog of the Liouville theorem is proved. Bibliography: 9 titles.

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 198; no. 5; pp. 564 - 574
Main Authors Kuzovatov, V. I., Kytmanov, A. M.
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.05.2014
Springer
Subjects
Mathematics
Mathematics and Statistics
Analytic Function
Harmonic Function
Integral Equation
Entire Space
Helmholtz Equation
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Summary:We establish the symmetry principle for solutions to the Helmholtz equation in a halfspace. The proof is based on the extension of the solution from the upper half-space to the entire space. An analog of the Liouville theorem is proved. Bibliography: 9 titles.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-014-1808-0