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- W4380997967 abstract "We investigate the half-space Dirichlet problem with summable boundary-value functions for an elliptic equation with an arbitrary amount of potentials undergoing translations in arbitrary directions. In the classical case of partial differential equations, the half-space Dirichlet problem for elliptic equations attracts great interest from researchers due to the following phenomenon: the solutions acquire qualitative properties specific for nonstationary (more exactly, parabolic) equations. In this paper, such a phenomenon is studied for nonlocal generalizations of elliptic differential equations, more exactly, for elliptic differential-difference equations with nonlocal potentials arising in various applications not covered by the classical theory. We find a Poisson-like kernel such that its convolution with the boundary-value function satisfies the investigated problem, prove that the constructed solution is infinitely smooth outside the boundary hyperplane, and prove its uniform power-like decay as the timelike independent variable tends to infinity." @default.
- W4380997967 created "2023-06-17" @default.
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- W4380997967 date "2023-06-14" @default.
- W4380997967 modified "2023-09-27" @default.
- W4380997967 title "Differential-Difference Elliptic Equations with Nonlocal Potentials in Half-Spaces" @default.
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- W4380997967 doi "https://doi.org/10.3390/math11122698" @default.
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