On normal solvability of a Dirichlet-type problem for a third-order improperly elliptic equation

摘要

We consider a Dirichlet-type problem in the upper half-plane for the improperly elliptic equation, u _(zz?) = 0, with boundary functions from the class L ~1(ρ) (ρ = (1 + {pipe}x{pipe}) ~(-α), α ≥ 0). The solutions of the problem are obtained in explicit form.