Resolvent estimates for elliptic systems in function spaces of higher regularity
R. Denk and M. Dreher
Abstract.
We consider parameter-elliptic boundary value problems and uniform
a priori estimates in Lp-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.
Electron. J. Diff. Equ.
2011(109)
1-12.
A preliminary version of the paper is available
here.
