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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2013, Volume 283, Pages 115–120
DOI: https://doi.org/10.1134/S0371968513040080 (Mi tm3511) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Necessary and sufficient conditions for a generalized solution to the initial-boundary value problem for the wave equation to belong to $W^1_p$ with $p\geq1$

V. A. Il'inab, A. A. Kuleshova

a Lomonosov Moscow State University, Moscow, Russia
b Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia
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DOI: https://doi.org/10.1134/S0371968513040080
Abstract: We establish necessary and sufficient conditions on the boundary function under which a generalized solution to the initial–boundary value problem for the wave equation with boundary conditions of the first kind belongs to $W^1_p$.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-12472-ofi_m
12-01-13113-ofi-m-rzhd
12-01-31169-mol_a
Ministry of Education and Science of the Russian Federation 8209
MK-4626.2013.1
This work was supported by the Russian Foundation for Basic Research (project nos. 13-01-12472-ofi_m2, 12-01-13113-ofi-m-rzhd, and 12-01-31169-mol_a), by the Ministry of Education and Science of the Russian Federation (project no. 8209), and by a grant of the President of the Russian Federation (project no. MK-4626.2013.1).
Received in February 2013
English version:
Proceedings of the Steklov Institute of Mathematics, 2013, Volume 283, Pages 110–115
DOI: https://doi.org/10.1134/S0081543813080087
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: V. A. Il'in, A. A. Kuleshov, “Necessary and sufficient conditions for a generalized solution to the initial-boundary value problem for the wave equation to belong to $W^1_p$ with $p\geq1$”, Function theory and equations of mathematical physics, Collected papers. In commemoration of the 90th anniversary of Lev Dmitrievich Kudryavtsev's birth, Trudy Mat. Inst. Steklova, 283, MAIK Nauka/Interperiodica, Moscow, 2013, 115–120; Proc. Steklov Inst. Math., 283 (2013), 110–115
Citation in format AMSBIB
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\by V.~A.~Il'in, A.~A.~Kuleshov
\paper Necessary and sufficient conditions for a~generalized solution to the initial-boundary value problem for the wave equation to belong to $W^1_p$ with~$p\geq1$
\inbook Function theory and equations of mathematical physics
\bookinfo Collected papers. In commemoration of the 90th anniversary of Lev Dmitrievich Kudryavtsev's birth
\serial Trudy Mat. Inst. Steklova
\yr 2013
\vol 283
\pages 115--120
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3511}
\crossref{https://doi.org/10.1134/S0371968513040080}
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\elib{https://elibrary.ru/item.asp?id=20783233}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2013
\vol 283
\pages 110--115
\crossref{https://doi.org/10.1134/S0081543813080087}
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    • This publication is cited in the following 2 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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