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The discrete dirichlet problem. Solvability and approximation properties

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We consider the discrete Dirichlet boundary value problem for a discrete elliptic pseudodifferential equation in the quadrant and study its solvability in discrete counterparts of the Sobolev–Slobodetskii space. The study is based on a special factorization of the elliptic symbol. We compare the solutions to the discrete Dirichlet problem and its continuous counterpart.

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Authors and Affiliations

  1. National Research University “Belgorod State University”, 85, Pobedy St., Belgorod, 308015, Russia

    A. V. Vasilyev, V. B. Vasilyev & A. A. Khodyreva

Authors
  1. A. V. Vasilyev
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  2. V. B. Vasilyev
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  3. A. A. Khodyreva
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Correspondence to V. B. Vasilyev.

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Translated from Problemy Matematicheskogo Analiza 123, 2023, pp. 31-40.

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Vasilyev, A.V., Vasilyev, V.B. & Khodyreva, A.A. The discrete dirichlet problem. Solvability and approximation properties. J Math Sci 270, 654–664 (2023). https://doi.org/10.1007/s10958-023-06377-2

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  • DOI: https://doi.org/10.1007/s10958-023-06377-2

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