Regularity of solutions to the Robin problem for differential-difference equations

This paper is devoted to the study of the qualitative properties of solutions to boundary-value problems for strongly elliptic differential-difference equations. In contrast to elliptic differential equation, the smoothness of generalized solutions of boundary-value problems for differential-difference equations can be violated near the boundary of these subdomains even for infinitely differentiable right-hand side. Here subdomains are defined as connected components of the set, which is obtained from the domain Q by throwing out all possible translations of the boundary (Formula presented.) by vectors of a certain group generated by translations occurring in the difference operators. We obtain necessary and sufficient conditions of smoothness of generalized solutions to the Robin problem for such equations on a boundary of neighbouring subdomains. © 2020 Informa UK Limited, trading as Taylor & Francis Group.