Riemann problem for multiply connected domain in Besov spaces-Reference-Cited by-同舟云学术

Riemann problem for multiply connected domain in Besov spaces

Published:2024-06-05 Issue:1 Volume:2024 Page:
ISSN:1687-2770
Container-title:Boundary Value Problems
language:en
Short-container-title:Bound Value Probl

Author:

Bliev Nazarbay,Yerkinbayev Nurlan

Abstract

AbstractIn 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.

Funder

Committee of Science of the Ministry of Science and Higher Education of the Republic of Kazakhstan

European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie, project SOMPATY

Publisher

Springer Science and Business Media LLC

Link

https://link.springer.com/content/pdf/10.1186/s13661-024-01883-x.pdf

Reference10 articles.

1. Averyanov, G.N., Soldatov, A.P.: Linear conjugation problem with a triangular matrix coefficient. J. Math. Sci. 257(1) (2021)

2. Begehr, H., Dai, D.-Q.: On continuous solutions of generalized Cauchy–Riemann system with more than one singularity. J. Differ. Equ. 196(1), 67–90 (2004)

3. Besov, O.V., Il’in, V.P., Nikol’skiĭ, S.M.: Integral Representations of Function and Embedding Theorems. “Nauka”, Moscow (1975). English translation edited by V.H. Winston and Sons, Washington, DC; Halsted Press, New York etc., 1978, 1979

4. Bliev, N.: Generalized Analytic Functions in Fractional Spaces (1985). English translation edited by H. Begehr and R. Radok: Addison Wesley Longman Inc, 1997

5. Gakhov, F.D.: Boundary Value Problems. Fizmatgiz, Moscow (1963). (in Russian); English translation edited by I.N. Sneddon, Pergamon Press, Oxford, 1966