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Mat. Zametki, 2007, Volume 82, Issue 3, Pages 323–334 (Mi mz3846)  

This article is cited in 5 scientific papers (total in 5 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

DOI: https://doi.org/10.4213/mzm3846

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

Bibliographic databases:

UDC: 517.5
Received: 10.11.2006

Citation: E. A. Balova, “Optimal Reconstruction of the Solution of the Dirichlet Problem from Inaccurate Input Data”, Mat. Zametki, 82:3 (2007), 323–334; Math. Notes, 82:3 (2007), 285–294

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “Optimal recovery of the solution of the heat equation from inaccurate data”, Sb. Math., 200:5 (2009), 665–682  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “On the reconstruction of convolution-type operators from inaccurate information”, Proc. Steklov Inst. Math., 269 (2010), 174–185  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    3. Balova E.A., “On the Optimal Reconstruction of a Solution of the Poisson Equation”, Differ. Equ., 50:1 (2014), 39–46  crossref  mathscinet  zmath  isi  elib  scopus
    4. E. A. Balova, K. Yu. Osipenko, “Optimal Recovery Methods for Solutions of the Dirichlet Problem that are Exact on Subspaces of Spherical Harmonics”, Math. Notes, 104:6 (2018), 781–788  mathnet  crossref  crossref  isi  elib
    5. G. G. Magaril-Il'yaev, E. O. Sivkova, “Optimal recovery of semi-group operators from inaccurate data”, Eurasian Math. J., 10:4 (2019), 75–84  mathnet  crossref
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