Maximal Regular Abstract Elliptic Equations and Applications

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Date

2010

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Volume Title

Publisher

Maik Nauka/interperiodica/springer

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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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Keywords

boundary value problem, operator differential equation, completeness of root elements, Banach-valued function spaces, operator-valued multipliers, interpolation of Banach spaces, semigroup of operators

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Citation

6

WoS Q

Q4

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Q3

Source

Volume

51

Issue

5

Start Page

935

End Page

948