Abstract
The 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.
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Original Russian Text Copyright © 2010 Shakhmurov V. B.
Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 5, pp. 1175–1191, September-October, 2010
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Shakhmurov, V.B. Maximal Regular Abstract Elliptic Equations and Applications. Sib Math J 51, 935–948 (2010). https://doi.org/10.1007/s11202-010-0093-5
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DOI: https://doi.org/10.1007/s11202-010-0093-5