2019
Том 71
№ 11

All Issues

Petkov I. V.

Articles: 2
Article (Russian)

On the Dirichlet problem for the Beltrami equations in finitely connected domains

Kovtonyuk D. A., Petkov I. V., Ryazanov V. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 7. - pp. 932-944

We establish a series of criteria for the existence of regular solutions of the Dirichlet problem for degenerate Beltrami equations in arbitrary Jordan domains. We also formulate the corresponding criteria for the existence of pseudoregular and multivalued solutions of the Dirichlet problem in the case of finitely connected domains.

Article (Russian)

On the boundary behavior of solutions of the Beltrami equations

Kovtonyuk D. A., Petkov I. V., Ryazanov V. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 8. - pp. 1078-1091

We show that every homeomorphic solution of the Beltrami equation $\overline{\partial} f = \mu \partial f$ in the Sobolev class $W^{1, 1}_{\text{loc}}$ is a so-called lower $Q$-homeomorphism with $Q(z) = K_{\mu}(z)$, where $K_{\mu}$ is a dilatation quotient of this equation. On this basis, we develop the theory of the boundary behavior and the removability of singularities of these solutions.