Abstract
The Dirichlet problem in the half-space for elliptic differential-difference equations with operators that are compositions of differential and difference operators is considered. For this problem, classical solvability or solvability almost everywhere (depending on the constraints imposed on the boundary data) is proved, an integral representation of the found solution in terms of a Poisson-type formula is constructed, and its convergence to zero as the time-like independent variable tends to infinity is proved.
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Acknowledgments
The author wishes to express deep gratitude to A. L. Skubachevskii for his permanent attention to this work.
Funding
This work was supported by the RUDN Program “5-100” (Secs. 1, 2) and by the Russian Foundation for Basic Research under grant 20-01-00288 A (Secs. 3, 4).
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Muravnik, A.B. Elliptic Differential-Difference Equations in the Half-Space. Math Notes 108, 727–732 (2020). https://doi.org/10.1134/S0001434620110115
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DOI: https://doi.org/10.1134/S0001434620110115