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 
@article{MZM_2007_82_3_a0,
     author = {E. A. Balova},
     title = {Optimal {Reconstruction} of the {Solution} of the {Dirichlet} {Problem} from {Inaccurate} {Input} {Data}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {323--334},
     publisher = {mathdoc},
     volume = {82},
     number = {3},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_3_a0/}
}
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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/