Smoothness of solutions to the mixed problem for elliptic differential-difference equation in cylinder

This article deals with mixed boundary value problem for an elliptic differential-difference equation in a cylinder. There are obtained results on the smoothness of generalized solutions of such problem in subdomains, and necessary and sufficient conditions for the preservation of smoothness on the boundaries of neighboring subdomains. © 2020 Informa UK Limited, trading as Taylor & Francis Group.