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Mat. Zametki, 2021, Volume 110, Issue 1, Pages 90–98 (Mi mz13009)  

Elliptic Differential-Difference Equations of General Form in the Half-Space

A. B. Muravnik

"Sozvezdie"

Abstract: We study the Dirichlet problem in the half-space for elliptic differential-difference equations with operators that are compositions of differential operators and shift operators not bound by commensurability conditions for shifts. For this problem, we establish classical solvability or solvability almost everywhere (depending on the constraints imposed on the boundary data), construct an integral representation of the solution by means of a Poisson-type formula, and prove that it approaches to zero as the time-like independent variable tends to infinity.

Keywords: differential-difference equations, elliptic problems, incommensurable shifts.

Funding Agency Grant Number
Russian Foundation for Basic Research 20-01-00288 A
This work was supported by the Russian Foundation for Basic Research under grant 20-01-00288 A.


DOI: https://doi.org/10.4213/mzm13009

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English version:
Mathematical Notes, 2021, 110:1, 92–99

Bibliographic databases:

UDC: 517.956
Received: 14.01.2021
Revised: 04.03.2021

Citation: A. B. Muravnik, “Elliptic Differential-Difference Equations of General Form in the Half-Space”, Mat. Zametki, 110:1 (2021), 90–98; Math. Notes, 110:1 (2021), 92–99

Citation in format AMSBIB
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\paper Elliptic Differential-Difference Equations of General Form in the Half-Space
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\issue 1
\pages 90--98
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\pages 92--99
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