Sobolev problem in the complete scale of Banach Spaces

Abstract

In a bounded domainG ⊂ ℝ ⁿ , whose boundary is the union of manifolds of different dimensions, we study the Sobolev problem for a properly elliptic expression of order 2m. The boundary conditions are given by linear differential expressions on manifolds of different dimensions. We study the Sobolev problem in the complete scale of Banach spaces. For this problem, we prove the theorem on a complete set of isomorphisms and indicate its applications.