Elliptic boundary-value problem in a two-sided improved scale of spaces
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.
English version (Springer): Ukrainian Mathematical Journal 60 (2008), no. 4, pp 574-597.
Citation Example: Mikhailets V. A., Murach A. A. Elliptic boundary-value problem in a two-sided improved scale of spaces // Ukr. Mat. Zh. - 2008. - 60, № 4. - pp. 497–520.