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Tr. Mat. Inst. Steklova, 2013, Volume 283, Pages 115–120 (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

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).


DOI: https://doi.org/10.1134/S0371968513040080

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English version:
Proceedings of the Steklov Institute of Mathematics, 2013, 283, 110–115

Bibliographic databases:

UDC: 517.9
Received in February 2013

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, Tr. Mat. Inst. Steklova, 283, MAIK Nauka/Interperiodica, Moscow, 2013, 115–120; Proc. Steklov Inst. Math., 283 (2013), 110–115

Citation in format AMSBIB
\Bibitem{IliKul13}
\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 Tr. 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}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3479951}
\elib{http://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}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000330983000007}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. A. Il'in, A. A. Kuleshov, “Equivalence of two definitions of a generalized $L_p$ solution to the initial-boundary value problem for the wave equation”, Proc. Steklov Inst. Math., 284 (2014), 155–160  mathnet  crossref  crossref  isi  elib  elib
    2. I. S. Mokrousov, “Kriterii prinadlezhnosti klassu $W^l_p$ obobschennogo iz klassa $L_p$ resheniya volnovogo uravneniya”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 18:3 (2018), 297–304  mathnet  crossref  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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