Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 109, pp. 1-12.

Title: Resolvent estimates for elliptic systems in
       function spaces of higher regularity
       
Authors: Robert Denk    (Univ. of Konstanz, Germany)
         Michael Dreher (Univ. of Konstanz, Germany)

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.