| Title | On the regular solutions of the Dirichlet problem for Beltrami equations |
| Publication Type | Journal Article |
| Year of Publication | 2014 |
| Authors | Kovtonyuk, DA, Petkov, IV, Ryazanov, VI |
| Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
| DOI | 10.15407/dopovidi2014.03.013 |
| Issue | 3 |
| Section | Mathematics |
| Pagination | 13-17 |
| Date Published | 3/2014 |
| Language | Russian |
| Abstract | The criteria of existence of regular solutions of the Dirichlet problem for degenerate Beltrami equations of the first kind in arbitrary Jordan domains with the boundary functions admitting at most a countable number of discontinuity points are established. In particular, the existence of regular solutions for arbitrary boundary functions of bounded variation is proved. |
| Keywords | Beltrami equations, Dirichlet problem, solutions |
1. Kovtonyuk D. A., Petkov I. V., Ryazanov V. I. Dopov. Nac. akad. nauk Ukr., 2012, No. 6: 30–33 (in Russian).
2. Kovtonyuk D. A., Petkov I. V., Ryazanov V. I. Ukr. mat. zhurn., 2012, 64, No. 7: 932–944 (in Russian).
3. Bojarski B., Gutlyanskii V., Ryazanov V. Ukr. mat. vestn., 2012, 9, No. 4: 460–476.
4. Goluzin G. M. Geometric theory of functions of a complex variable. Moscow: Nauka, 1966 (in Russian).
5. Ignatiev A. A., Riazanov V. I. Ukr. mat. vestn., 2005, 2, No.3: 395–417.
6. Ryazanov V., Srebro U., Yakubov E. Complex Var. Elliptic Equat., 2010, 55, No. 1–3: 219–236. https://doi.org/10.1080/17476930903100417
7. Gutlyanskii V., Ryazanov V., Srebro U., Yakubov E. The Beltrami equation: a geometric approach. In: Developments in Mathematics; Vol. 26. New York: Springer, 2012. https://doi.org/10.1007/978-1-4614-3191-6
8. Martio O., Ryazanov V., Srebro U., Yakubov E. Moduli in modern mapping theory. New York: Springer, 2009.
