Abstract
We consider the problem of solvability of an inhomogeneous Dirichlet problem for a scalar improperly elliptic differential equation with complex coefficients in a bounded domain. A model case where the unit disk is chosen as the domain and the equation does not contain lower terms is studied. We prove that the classes of Dirichlet data for which the problem has a unique solution in the Sobolev space are spaces of functions with exponentially decreasing Fourier coefficients.
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