Regular elliptic boundary-value problem for a homogeneous equation in a two-sided improved scale of spaces

Abstract

We study a regular elliptic boundary-value problem for a homogeneous differential equation in a bounded domain. We prove that the operator of this problem is a Fredholm (Noether) operator in a two-sided improved scale of functional Hilbert spaces. The elements of this scale are Hörmander-Volevich-Paneyakh isotropic spaces. We establish an a priori estimate for a solution and investigate its regularity.