2019
Том 71
№ 11

All Issues

Tsvetkov E. L.

Articles: 2
Article (Russian)

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

Tsvetkov E. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1995. - 47, № 1. - pp. 93–104

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 .

Article (Russian)

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

Tsvetkov E. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1993. - 45, № 8. - pp. 1140–1150

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 $Q_r$.