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On the optimal reconstruction of a solution of the Poisson equation

  • Partial Differential Equations
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Abstract

We consider the problem of optimal reconstruction of a solution of the generalized Poisson equation in a bounded domain Q with homogeneous boundary conditions for the case in which the right-hand side of the equation is fuzzy. We assume that right-hand sides of the equations belong to generalized Sobolev classes and finitely many Fourier coefficients of the right-hand sides of the equations are known with some accuracy in the Euclidean metric. We find the optimal reconstruction error and construct a family of optimal reconstruction methods. The problem on the best choice of the coefficients to be measured is solved.

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Authors and Affiliations

  1. Russian State University of Technology, Moscow, Russia

    E. A. Balova

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  1. E. A. Balova
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Correspondence to E. A. Balova.

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Original Russian Text © E.A. Balova, 2014, published in Differentsial’nye Uravneniya, 2014, Vol. 50, No. 1, pp. 41–48.

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Balova, E.A. On the optimal reconstruction of a solution of the Poisson equation. Diff Equat 50, 39–46 (2014). https://doi.org/10.1134/S0012266114010066

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  • DOI: https://doi.org/10.1134/S0012266114010066

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