On the dirichlet problem for an improperly elliptic equation
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.
English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 2, pp 187-195.
Citation Example: Burskii V. P., Kirichenko E. V. On the dirichlet problem for an improperly elliptic equation // Ukr. Mat. Zh. - 2011. - 63, № 2. - pp. 156-164.