This article is cited in 9 papers

Optimal Reconstruction of the Solution of the Dirichlet Problem from Inaccurate Input Data

E. A. Balova

Moscow State Aviation Technological University

Abstract: In this paper, we consider the optimal reconstruction of the solution of the Dirichlet problem in the $d$-dimensional ball on the sphere of radius $r$ from inaccurately prescribed traces of the solution on the spheres of radii $R_1$ and $R_2$, where $R_1<r<R_2$. We also study the optimal reconstruction of the solution of the Dirichlet problem in the $d$-dimensional ball from a finite collection of Fourier coefficients of the boundary function which are prescribed with an error in the mean-square and uniform metrics.

Keywords: Dirichlet problem, optimal reconstruction, inaccurate input data, Lagrange function, Beltrami–Laplace operator, Sobolev space.

UDC: 517.5

Received: 10.11.2006

DOI: 10.4213/mzm3846

 English version: Mathematical Notes, 2007, 82:3, 285–294

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