Эллиптические краевые задачи в многосвязной области в уточненной шкале пространств

Abstract

A mixed elliptic boundary-value problem for a differential equation over a multiply connected bounded domain is studied. The boundary conditions have different orders on the distinct connected components of the boundary. We prove that the operator of the problem is a Fredholm one on the one-sided refined scale of functional Hilbert spaces. Elements of this scale are the isotropic spaces of Hormander–Volevich–Paneyakh. A mixed elliptic boundary-value problem with parameter is investigated as well.