Neumann problem and one oblique-derivative problem for an improperly elliptic equation
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.
English version (Springer): Ukrainian Mathematical Journal 64 (2012), no. 4, pp 511-524.
Citation Example: Burskii V. P., Lesina E. V. Neumann problem and one oblique-derivative problem for an improperly elliptic equation // Ukr. Mat. Zh. - 2012. - 64, № 4. - pp. 451-462.