Elliptic Equations with Translations of General Form in a Half-Space
Matematičeskie zametki, Tome 111 (2022) no. 4, pp. 571-580
Voir la notice de l'article provenant de la source Math-Net.Ru
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.
Keywords:
differential-difference equations, elliptic problems in a half-space, translations with respect to arbitrary variables.
@article{MZM_2022_111_4_a8,
author = {A. B. Muravnik},
title = {Elliptic {Equations} with {Translations} of {General} {Form} in a {Half-Space}},
journal = {Matemati\v{c}eskie zametki},
pages = {571--580},
publisher = {mathdoc},
volume = {111},
number = {4},
year = {2022},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2022_111_4_a8/}
}
A. B. Muravnik. Elliptic Equations with Translations of General Form in a Half-Space. Matematičeskie zametki, Tome 111 (2022) no. 4, pp. 571-580. http://geodesic.mathdoc.fr/item/MZM_2022_111_4_a8/