We study the problem of solvability of the inhomogeneous third boundary-value problem in a bounded domain for a scalar improperly elliptic differential equation with complex coefficients and homogeneous symbol. It is shown that this problem has a unique solution in the Sobolev space over the circle for special classes of boundary data from the spaces of functions with exponentially decreasing Fourier coefficients.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 2, pp. 279–283, February, 2014.
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Burskii, V.P., Lesina, E.V. On the Third Boundary-Value Problem for an Improperly Elliptic Equation in a Disk. Ukr Math J 66, 311–316 (2014). https://doi.org/10.1007/s11253-014-0931-x
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DOI: https://doi.org/10.1007/s11253-014-0931-x