On regularity of generalized solutions of the third boundary-value problem for an elliptic difference-differential equation

Unlike the case of elliptic differential equations, generalized solutions of elliptic difference-differential equations may be not smooth in a domainQ but remain smooth only in certain subdomainsQ _r Q Conditions are considered which are necessary and sufficient for generalized solutions of the third boundary-value problem to preserve smoothness on the boundary of adjacent subdomainsQ _r .Translated from Ukrainskii Matematicheskii Zhurnal, Vol.47, No. 1, pp. 93–104, January, 1995.The author expresses his deep gratitude to A. D. Myshkis and A. L. Skubachevskii for helpful discussions.