Optimal recovery of the solution to the Dirichlet problem in the half-plane

E. V. Abramova^a, E. O. Sivkova<sup>ba

a</sup> National Research University "Moscow Power Engineering Institute"
^b Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz

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.

UDC: 517.51

MSC: 35R30

Received: 28.12.2022
Revised: 04.02.2023
Accepted: 10.02.2023

DOI: 10.33048/smzh.2023.64.301

 English version: Siberian Mathematical Journal, 2023, 64:3, 507–513