On the theory of the boundary behavior of mappings of the Sovolev class on Riemann surfaces

Authors

  • S.V. Volkov nstitute of Applied Mathematics and Mechanics of the NAS of Ukraine, Slovyansk
  • V.Y. Ryazanov nstitute of Applied Mathematics and Mechanics of the NAS of Ukraine, Slovyansk

DOI:

https://doi.org/10.15407/dopovidi2016.10.005

Keywords:

boundary behavior, homeomorphic extension, Riemann surfaces, Sobolev classes, weakly flat boundaries

Abstract

In terms of dilatations, a number of criteria for a homeomorphic extension to the boundary of mappings in the Sobolev class between domains on Riemann surfaces are formulated.

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References

Kovtonyuk D.A., Petkov Y.V., Ryazanov V.Y. Ukr. mat. zhurn., 2011, 63, No 8: 1078-1091 (in Russian).

Kovtonyuk D.A., Petkov Y.V., Ryazanov V.Y. Ukr. mat. zhurn., 2012, 64, No 7: 932-944 (in Russian).

Kovtonyuk D.A., Petkov Y.V., Ryazanov V.Y., Salymov R.R. Alhebra i Analyz, 2013, 25, Iss. 4: 101-124 (in Russian).

Forster O. Rymanovy poverkhnosty, Moscow: Mir, 1980 (in Russian).

Stoylov S. Lektsyy o topolohycheskykh pryntsypakh teoryy analytycheskykh funktsyy, Moscow: Nauka, 1964 (in Russian).

Kovtonyuk D.A., Ryazanov V.Y. Ukr. mat. vestnyk, 2008, 5, No 2: 159-184 (in Russian).

Ryazanov V.Y., Salymov R.R. Ukr. mat. vestnyk, 2007, 4, No 2: 199-234 (in Russian).

Martio O., Ryazanov V., Srebro U., Yakubov E. Moduli in Modern Mapping Theory, New York: Springer, 2009.

Kuratovskyy K. Topolohyya, T. 1, Moscow: Mir, 1966 (in Russian).

Yhnat'ev A. A., Ryazanov V.Y. Ukr. mat. vestnyk, 2005, 2, No 3: 395-417 (in Russian).

Published

23.12.2024

How to Cite

Volkov, S., & Ryazanov, V. (2024). On the theory of the boundary behavior of mappings of the Sovolev class on Riemann surfaces . Reports of the National Academy of Sciences of Ukraine, (10), 5–9. https://doi.org/10.15407/dopovidi2016.10.005