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Mat. Zametki, 2018, Volume 104, Issue 6, Pages 803–811 (Mi mz11784)  

Optimal Recovery Methods for Solutions of the Dirichlet Problem that are Exact on Subspaces of Spherical Harmonics

E. A. Balovaa, K. Yu. Osipenkobc

a Moscow Aviation Institute (National Research University)
b Lomonosov Moscow State University
c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow

Abstract: We consider the optimal recovery problem for the solution of the Dirichlet problem for the Laplace equation in the unit $d$-dimensional ball on a sphere of radius $\rho$ from a finite collection of inaccurately specified Fourier coefficients of the solution on a sphere of radius $r$, $0<r<\rho<1$. The methods are required to be exact on certain subspaces of spherical harmonics.

Keywords: optimal recovery, Dirichlet problem, Laplace equation, spherical harmonics.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00649
This work was supported by the Russian Foundation for Basic Research under grant 17-01-00649.


DOI: https://doi.org/10.4213/mzm11784

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English version:
Mathematical Notes, 2018, 104:6, 781–788

Bibliographic databases:

Document Type: Article
UDC: 517.51
Received: 29.08.2017

Citation: E. A. Balova, K. Yu. Osipenko, “Optimal Recovery Methods for Solutions of the Dirichlet Problem that are Exact on Subspaces of Spherical Harmonics”, Mat. Zametki, 104:6 (2018), 803–811; Math. Notes, 104:6 (2018), 781–788

Citation in format AMSBIB
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