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.
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Abramova E.V., Magaril-Il’yaev G.G. and Sivkova E.O., “Best recovery of the solution of the Dirichlet problem in a half-space from inaccurate data,” Comp. Math. Math. Phys., vol. 60, no. 10, 1656–1665 (2020).
Acknowledgment
The authors are grateful to G.G. Magaril-Il’yaev for useful discussions.
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Translated from Sibirskii Matematicheskii Zhurnal, 2023, Vol. 64, No. 3, pp. 441–449. https://doi.org/10.33048/smzh.2023.64.301
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Abramova, E.V., Sivkova, E.O. Optimal Recovery of the Solution to the Dirichlet Problem in the Half-Plane. Sib Math J 64, 507–513 (2023). https://doi.org/10.1134/S0037446623030011
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DOI: https://doi.org/10.1134/S0037446623030011