On the Sobolev problem in the complete scale of Banach spaces

In a bounded domainG with boundary ∂G that consists of components of different dimensions, we consider an elliptic boundary-value problem in complete scales of Banach spaces. The orders of boundary expressions are arbitrary; they are pseudodifferential along ∂G. We prove the theorem on a complete set of isomorphisms and generalize its application. The results obtained are true for elliptic Sobolev problems with a parameter and parabolic Sobolev problems as well as for systems with the Douglis-Nirenberg structure. Chernigov Pedagogical Institute, Chernigov. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 9, pp. 1181–1192, September, 1999.