On a certain property of a regular difference operator with variable coefficients

We consider a regular difference operator with variable coefficients in a bounded domain. It will be proved that this operator maps continuously and bijectively the Sobolev space of order k with the homogeneous Dirichlet boundary conditions to the subspace of Sobolev space of order k with nonlocal boundary conditions on the shifts of the boundary. This allows to apply the results obtained for nonlocal elliptic problems to the investigation of elliptic differential-difference equations. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.

Editors
-
Publisher
-
Number of issue
5
Language
English
Pages
852-865
Status
Published
Department
-
Number
-
Volume
64
Year
2019
Organizations
  • 1 Peoples' Friendship University of Russia (RUDN-University), Moscow, Russian Federation
Keywords
39A14; 39A70; A. Soldatov; difference operators; Elliptic differential-difference equations; generalized solutions; nonlocal elliptic problems
Date of creation
19.07.2019
Date of change
19.07.2019
Short link
https://repository.rudn.ru/en/records/article/record/38644/