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 $\mathrm{\partial }Q$ 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.

本文致力于研究强椭圆微分方程边值问题解的定性性质。与椭圆微分方程相比，微分微分方程边值问题的广义解的平滑性可能在这些子域的边界附近被破坏，即使对于无限可微的右手边也是如此。这里的子域被定义为集合的连通分量，它是通过抛出边界的所有可能平移从域Q中获得的$\mathrm{\partial }问$通过在差分算子中发生的平移生成的某个组的向量。对于相邻子域边界上的此类方程，我们获得了 Robin 问题的广义解平滑的充分必要条件。