Robert Denk, Michael Dreher
Abstract:
We consider parameter-elliptic boundary value problems and
uniform a priori estimates in
-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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