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.
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.
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.