A Boundary Value Problem for Bitsadze Equation in the Unit Disc

摘要

A boundary value problem for the Bitsadze equation (partial deriv)~2/(partial deriv)z~2 u(x,y)≡1/4 (partial deriv/partial deriv x) + ipartial deriv/partial deriv y)~2 u(x,y)= 0 in the interior of the unit disc is considered. It is proved that the problem is Noetherian and its index is calculated, and solvability conditions lor the non-homogeneous problem are proposed. Some solutions of the homogeneous problem are explicitely found.