Neumann problem and one oblique-derivative problem for an improperly elliptic equation

Abstract

We investigate the solvability of an inhomogeneous Neumann problem and oblique-derivative problem for an improperly elliptic scalar differential equation with complex coefficients in a bounded domain. The model case where the domain is the unit disk and the equation does not have lower-order terms is studied. It is proved that the classes of boundary data for which the problems have unique solutions in a Sobolev space are the spaces of functions with exponentially decreasing Fourier coefficients.