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

Unlike the case of elliptic differential equations, generalized solutions of elliptic differential-difference equations may be nonsmooth on an entire domainQ, only preserving smoothness on certain subdomainsQ _r Q. The conditions are considered under which the generalized solutions of the third boundary-value problem remain smooth on the boundaries of the neighboring subdomainsQ _r .Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 8, pp. 1140–1150, August, 1993.The author is grateful to A. D. Myshkis and A. L. Skubachevaskii for their kind attention to the work and valuable advice.