Electron. J. Diff. Equ., Vol. 2011 (2011), No. 109, pp. 1-12.

Resolvent estimates for elliptic systems in function spaces of higher regularity

Robert Denk, Michael Dreher

Abstract:
We consider parameter-elliptic boundary value problems and uniform a priori estimates in $L^p$-Sobolev spaces of Bessel potential and Besov type. The problems considered are systems of uniform order and mixed-order systems (Douglis-Nirenberg systems). It is shown that compatibility conditions on the data are necessary for such estimates to hold. In particular, we consider the realization of the boundary value problem as an unbounded operator with the ground space being a closed subspace of a Sobolev space and give necessary and sufficient conditions for the realization to generate an analytic semigroup.

Submitted January 11, 2011. Published August 25, 2011.
Math Subject Classifications: 35G45, 47D06.
Key Words: Parameter-ellipticity; Douglis-Nirenberg systems; analytic semigroups.

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Robert Denk
Department of Mathematics and Statistics
University of Konstanz
78457 Konstanz, Germany
email: robert.denk@uni-konstanz.de
Michael Dreher
Department of Mathematics and Statistics
University of Konstanz
78457 Konstanz, Germany
email: michael.dreher@uni-konstanz.de

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