Shakhmurov, V. B.2024-05-252024-05-25201060037-44661573-926010.1007/s11202-010-0093-52-s2.0-77958603041https://doi.org/10.1007/s11202-010-0093-5https://hdl.handle.net/20.500.14517/657The oblique derivative problem is addressed for an elliptic operator differential equation with variable coefficients in a smooth domain. Several conditions are obtained, guaranteing the maximal regularity, the Fredholm property, and the positivity of this problem in vector-valued L (p)-spaces. The principal part of the corresponding differential operator is nonselfadjoint. We show the discreteness of the spectrum and completeness of the root elements of this differential operator. These results are applied to anisotropic elliptic equations.eninfo:eu-repo/semantics/closedAccessboundary value problemoperator differential equationcompleteness of root elementsBanach-valued function spacesoperator-valued multipliersinterpolation of Banach spacessemigroup of operatorsArticleQ4Q3515935948WOS:000283300600017