Optimal Recovery Methods for Solutions of the Dirichlet Problem that are Exact on Subspaces of Spherical Harmonics
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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 ρ from a finite collection of inaccurately specified Fourier coefficients of the solution on a sphere of radius r, 0 < r < ρ < 1. The methods are required to be exact on certain subspaces of spherical harmonics.
Keywordsoptimal recovery Dirichlet problem Laplace equation spherical harmonics
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