Regular elliptic boundary-value problem for a homogeneous equation in a two-sided improved scale of spaces
AbstractWe 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.
How to Cite
Mikhailets, V. A., and A. A. Murach. “Regular Elliptic Boundary-Value Problem for a Homogeneous Equation in a Two-Sided Improved Scale of Spaces”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, no. 11, Nov. 2006, pp. 1536–1555, https://umj.imath.kiev.ua/index.php/umj/article/view/3553.