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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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