Riemann problem for multiply connected domain in Besov spaces
Bliev N. Yerkinbayev N.
December 2024Springer Science and Business Media Deutschland GmbH
Boundary Value Problems
2024#2024Issue 1
In this paper, we obtain conditions of the solvability of the Riemann boundary value problem for sectionally analytic functions in multiply connected domains in Besov spaces embedded into the class of continuous functions. We indicate a new class of Cauchy-type integrals, which are continuous on a closed domain with continuous (not Hölder) density in terms of Besov spaces, and for which the Sokhotski–Plemelj formulas are valid.
30H05 , 30H25 , 30H50 , 46E15 , Besov spaces , Cauchy-type integral , Riemann boundary value problem , Sectionally analytic functions
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Institute of Mathematics and Mathematical Modeling, 125 Pushkin str., Almaty, 050010, Kazakhstan
Al-Farabi Kazakh National University, 71 al-Farabi Ave., Almaty, 050040, Kazakhstan
Institut für Mathematik, Universität zu Lübeck, Ratzeburger Allee 160., Lübeck, 23562, Germany
Institute of Mathematics and Mathematical Modeling
Al-Farabi Kazakh National University
Institut für Mathematik
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