Elliptic boundary-value problem in a two-sided improved scale of spaces - Mikhailets, V. A.; Murach, A. A. (Ukrains’kyi Matematychnyi Zhurnal, 2008)
We study a regular elliptic boundary-value problem in a bounded domain with smooth boundary. We prove that the operator of this problem is a Fredholm one in a two-sided improved scale of functional Hilbert spaces and that it generates there a complete collection of isomorphisms. Elements of this scale are Hörmander-Volevich-Paneyakh isotropic spaces and some their modi.cations. An a priori estimate for a solution is obtained and its regularity is investigated.