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Sibirskii Matematicheskii Zhurnal, 2023, Volume 64, Number 3, Pages 441–449
DOI: https://doi.org/10.33048/smzh.2023.64.301 (Mi smj7773) 		 
Optimal recovery of the solution to the Dirichlet problem in the half-plane

E. V. Abramovaa, E. O. Sivkovaba

a National Research University "Moscow Power Engineering Institute"
b Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz
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DOI: https://doi.org/10.33048/smzh.2023.64.301
Abstract: We find a family of optimal methods for recovering the solution to the Dirichlet problem in the upper half-plane on a line parallel to the $x$-axis from an approximate measurement of this solution on another line under the condition that the boundary function lies in a certain Sobolev space.
Keywords: Dirichlet problem, optimal methods, Fourier transform.
Received: 28.12.2022
Revised: 04.02.2023
Accepted: 10.02.2023
English version:
Siberian Mathematical Journal, 2023, Volume 64, Issue 3, Pages 507–513
DOI: https://doi.org/10.1134/S0037446623030011
Document Type: Article
UDC: 517.51
MSC: 35R30
Language: Russian
Citation: E. V. Abramova, E. O. Sivkova, “Optimal recovery of the solution to the Dirichlet problem in the half-plane”, Sibirsk. Mat. Zh., 64:3 (2023), 441–449; Siberian Math. J., 64:3 (2023), 507–513
Citation in format AMSBIB
\Bibitem{AbrSiv23}
\by E.~V.~Abramova, E.~O.~Sivkova
\paper Optimal recovery of the solution to the Dirichlet problem in the half-plane
\jour Sibirsk. Mat. Zh.
\yr 2023
\vol 64
\issue 3
\pages 441--449
\mathnet{http://mi.mathnet.ru/smj7773}
\transl
\jour Siberian Math. J.
\yr 2023
\vol 64
\issue 3
\pages 507--513
\crossref{https://doi.org/10.1134/S0037446623030011}
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