Geodesic
Optimal Reconstruction of the Solution of the Dirichlet Problem from Inaccurate Input Data
Matematičeskie zametki, Tome 82 (2007) no. 3, pp. 323-334.

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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 $R_1$. 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, inaccurate input data, Lagrange function, Beltrami–Laplace operator, Sobolev space.
Mots-clés : optimal reconstruction 
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E. A. Balova. Optimal Reconstruction of the Solution of the Dirichlet Problem from Inaccurate Input Data. Matematičeskie zametki, Tome 82 (2007) no. 3, pp. 323-334. http://geodesic.mathdoc.fr/item/MZM_2007_82_3_a0/

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