Smoothness of generalized solutions of the third boundary-value problem for an elliptic differential-difference equation - Tsvetkov, E. L. (Ukrains’kyi Matematychnyi Zhurnal, 1993)
Unlike the case of elliptic differential equations, generalized solutions of elliptic differential-difference equations may be nonsmooth on an entire domain $Q$, only preserving smoothness on certain subdomains $Q_r \subset Q$. The conditions are considered under which the generalized solutions of the third boundary-value problem remain smooth on the boundaries of the neighboring subdomains $Q_r$.