Strongly elliptic differential-difference equations with mixed boundary conditions in a bounded domain

Abstract

We consider mixed boundary value problem for strongly elliptic differential-difference equation and nonlocal mixed problem for elliptic differential equation in a bounded domain. We establish the connection between these problems, prove theorems on the unique solvability and on the smoothness of generalized solutions of these problems.

Keywords:

• Elliptic differential-difference equation
• mixed boundary value problem
• generalized solution
• difference operator

AMS Subject Classifications:

• 39A70
• 39A14

Acknowledgments

The author thanks A. L. Skubachevskii for interest in the work and valuable advice.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work is supported by the Ministry of Science and Higher Education of the Russian Federation: agreement no. 075-03-2020-223/3 (FSSF-2020-0018).