2019
Том 71
№ 5

# Elliptic Operators in a Refined Scale of Functional Spaces

Abstract

We study the theory of elliptic boundary-value problems in the refined two-sided scale of the Hormander spaces $H^{s, \varphi}$, where $s \in R,\quad \varphi$ is a functional parameter slowly varying on $+\infty$. In the case of the Sobolev spaces $H^{s}$, the function $\varphi(|\xi|) \equiv 1$. We establish that the considered operators possess the properties of the Fredholm operators, and the solutions are globally and locally regular.

English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 5, pp 817-825.

Citation Example: Mikhailets V. A., Murach A. A. Elliptic Operators in a Refined Scale of Functional Spaces // Ukr. Mat. Zh. - 2005. - 57, № 5. - pp. 689–696.

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