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Matematicheskie Trudy, 2011, Volume 14, Number 2, Pages 189–205 (Mi mt221)  
The Poisson problem in a domain with a cut

Yu. N. Subbotinab, N. I. Chernykhab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg, Russia
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Abstract: With the help of harmonic wavelets, we study the behavior of solutions to the Poisson problem in an elliptic ring when the interior bound shrinks to a segment. It is demonstrated that only partial derivatives of a solution have unbounded singularities near the ends of this segment.
Key words: harmonic wavelets, elliptic ring, Laplace operator, Poisson boundary value problem.
Received: 16.05.2011
English version:
Siberian Advances in Mathematics, 2012, Volume 22, Issue 3, Pages 204–216
DOI: https://doi.org/10.3103/S1055134412030042
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: Yu. N. Subbotin, N. I. Chernykh, “The Poisson problem in a domain with a cut”, Mat. Tr., 14:2 (2011), 189–205; Siberian Adv. Math., 22:3 (2012), 204–216
Citation in format AMSBIB
\Bibitem{SubChe11}
\by Yu.~N.~Subbotin, N.~I.~Chernykh
\paper The Poisson problem in a~domain with a~cut
\jour Mat. Tr.
\yr 2011
\vol 14
\issue 2
\pages 189--205
\mathnet{http://mi.mathnet.ru/mt221}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2961774}
\transl
\jour Siberian Adv. Math.
\yr 2012
\vol 22
\issue 3
\pages 204--216
\crossref{https://doi.org/10.3103/S1055134412030042}
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