We study the problem of solvability of an inhomogeneous Neumann problem and an oblique-derivative problem for an improperly elliptic scalar differential equation with complex coefficients in a bounded domain. A model case in which the domain is a unit disk and the equation does not contain lower-order terms is investigated. It is shown that the classes of boundary data for which these problems are uniquely solvable in a Sobolev space are formed by the spaces of functions with exponentially decreasing Fourier coefficients.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 4, pp. 451–462, April, 2012.
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Burskii, V.P., Lesina, E.V. Neumann problem and one oblique-derivative problem for an improperly elliptic equation. Ukr Math J 64, 511–524 (2012). https://doi.org/10.1007/s11253-012-0662-9
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DOI: https://doi.org/10.1007/s11253-012-0662-9