# Lomako T.V.

### On The Boundary Behavior of Regular Solutions of the Degenerate Beltrami Equations

Ukr. Mat. Zh. - 2015. - 67, № 4. - pp. 489-498

We study the boundary behavior of regular solutions to the degenerate Beltrami equations with constraints of the integral type imposed on the coefficient.

### Theorem on Closure and the Criterion of Compactness for the Classes of Solutions of the Beltrami Equations

Ukr. Mat. Zh. - 2013. - 65, № 12. - pp. 1657–1666

We study the classes of regular solutions of degenerate Beltrami equations with constraints of the integral type imposed on a complex coefficient, prove the theorem on closure, and establish a criterion of compactness for these classes.

### On the theory of convergence and compactness for Beltrami equations with constraints of set-theoretic type

Ukr. Mat. Zh. - 2011. - 63, № 9. - pp. 1227-1240

We prove theorems on convergence and compactness for classes of regular solutions of degenerate Beltrami equations with set-theoretic constraints imposed on the complex coefficient and construct variations for these classes.

### On the theory of convergence and compactness for Beltrami equations

Ukr. Mat. Zh. - 2011. - 63, № 3. - pp. 341-340

The convergence and compactness theorems are proved for classes of regular solutions of the Beltrami degenerate equations with restrictions of integral type on the dilatation.

### On extension of some generalizations of quasiconformal mappings to a boundary

Ukr. Mat. Zh. - 2009. - 61, № 10. - pp. 1329-1337

This work is devoted to the investigation of ring $Q$-homeomorphisms. We formulate conditions for a function $Q(x)$ and the boundary of a domain under which every ring $Q$-homeomorphism admits a homeomorphic extension to the boundary. For an arbitrary ring $Q$-homeomorphism $f: D → D’$ with $Q ∈ L_1(D)$; we study the problem of the extension of inverse mappings to the boundary. It is proved that an isolated singularity is removable for ring $Q$-homeomorphisms if $Q$ has finite mean oscillation at a point.