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

Abstract

We consider Dirichlet type problem in upper half-plane for improperly elliptic equation $u_{z\bar{z}^2}=0$, with boundary functions from the class $L^1(\rho)$ $(\rho=(1+|x|)^{-\alpha}, \alpha\geq0)$. The solutions of the problem are obtained in explicit form.