Elliptic Equations with Translations of General Form in a Half-Space

Abstract: We study the Dirichlet problem in a half-space for elliptic differential-difference equations with operators representing superpositions of differential operators and translation operators. In each superposition, the second-derivative operator and the translation operator act with respect to arbitrary independent tangential (space-like) variables. For this problem, solvability in the sense of generalized functions (distributions) is established, an integral representation of the solution is constructed by means of a Poisson-type formula, its infinite smoothness outside the boundary hyperplane is proved, and its convergence to zero (together with all of its derivatives) as the time-like independent variable tends to infinity is established. © 2022, Pleiades Publishing, Ltd.

Authors
Number of issue
3-4
Language
English
Pages
587-594
Status
Published
Volume
111
Year
2022
Organizations
  • 1 Peoples’ Friendship University of Russia (RUDN University), Moscow, 117198, Russian Federation
Keywords
differential-difference equations; elliptic problems in a half-space; translations with respect to arbitrary variables
Date of creation
06.07.2022
Date of change
06.07.2022
Short link
https://repository.rudn.ru/en/records/article/record/83694/
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