@article{Burskii_Kirichenko_2011, title={On the dirichlet problem for an improperly elliptic equation}, volume={63}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/2707}, abstractNote={The solvability of the inhomogeneous Dirichlet problem in a bounded domain for scalar improperly elliptic differential equation with complex coefficients is investigated. We study a model case where the unit disk is chosen as a domain and the equation does not contain lowest terms. We prove that the problem has a unique solution in the Sobolev space for special classes of Dirichlet data that are spaces of functions with exponential decrease of the Fourier coefficients.}, number={2}, journal={Ukrainsâ€™kyi Matematychnyi Zhurnal}, author={Burskii, V. P. and Kirichenko, E. V.}, year={2011}, month={Feb.}, pages={156-164} }