Fredholm theory connected with a Douglis–Nirenberg system of differential equations over an exterior region in R n

We consider a boundary problem over an exterior subregion of R n for a Douglis–Nirenberg system of differential operators under limited smoothness asumptions and under the assumption of parameter‐ellipticity in a closed sector L in the complex plane with vertex at the origin. We pose the problem in an L p Sobolev–Bessel potential space setting, 1 < p < ∞ , and denote by A p the operator induced in this setting by the boundary problem under null boundary conditions. We then derive results pertaining to the Fredholm theory for A p for values of the spectral parameter λ lying in L as well as results pertaining to the invariance of the Fredholm domain of A p with p .