Elliptic boundary-value problems in complete scales of Nikol'skii-type spaces

Abstract

We consider an elliptic boundary-value problem on an infinitely smooth manifold with, generally speaking, disconnected boundary. It is established that the operator of this problem is a Fredholm operator when considered in complete scales of functional spaces that depend on the parameters s ε ℝ,pε[1, ∞] and, for sufficiently large s≥0, coincide with the classical Nikol'skii spaces on a manifold.