# Methods of Functional Analysis

and Topology

Editors-in-Chief: A. N. Kochubei,
Yu. G. Kondratiev

ISSN: 1029-3531 (Print) 2415-7503 (Online)

Founded by Yu. M. Berezansky in 1995.

Methods of Functional Analysis and Topology (MFAT), founded in 1995, is a peer-reviewed journal publishing original articles and surveys on general methods and techniques of functional analysis and topology with a special emphasis on applications to modern mathematical physics.

MFAT is an open access journal, free for authors and free for readers.

MFAT is indexed in: MathSciNet, zbMATH, Scopus, Web of Science, DOAJ, Google Scholar

## Latest Articles (June, 2020)

### Elliptic problems with unknowns on the boundary and irregular boundary data

Iryna Chepurukhina, Aleksandr Murach

Methods Funct. Anal. Topology **26** (2020), no. 2, 91-02

We consider an elliptic problem with unknowns on the boundary of the domain of the elliptic equation and suppose that the right-hand side of this equation is square integrable and that the boundary data are arbitrary (specifically, irregular) distributions. We investigate local (up to the boundary) properties of generalized solutions to the problem in Hilbert distribution spaces that belong to the refined Sobolev scale. These spaces are parametrized with a real number and a function that varies slowly at infinity. The function parameter refines the number order of the space. We prove theorems on local regularity and a local a priori estimate of generalized solutions to the problem under investigation. These theorems are new for Sobolev spaces as well.

### When universal separated graph $C^*$-algebras are exact

Methods Funct. Anal. Topology **26** (2020), no. 2, 126-140

We consider when the universal $C^*$-algebras associated to separated graphs are exact. Specifically, for finite separated graphs we show that the universal $C^*$-algebra is exact if and only if the $C^*$-algebra is isomorphic to a graph $C^*$-algebra which occurs precisely when the universal and reduced $C^*$-algebras of the separated graph are isomorphic.

### A condition for generalized solutions of a parabolic problem for a Petrovskii system to be classical

Methods Funct. Anal. Topology **26** (2020), no. 2, 111-118

We obtain a new sufficient condition under which generalized solutions to a parabolic initial boundary-value problem for a Petrovskii system and the homogeneous Cauchy data are classical. The condition is formulated in terms of the belonging of the right-hand sides of the problem to some anisotropic Hörmander spaces.

### Volodymyr Andriyovych Mikhailets (to 70th birthday anniversary)

Methods Funct. Anal. Topology **26** (2020), no. 2, 89-90