On the Riemann-Hilbert problem in multiply connected domains

Autor: Ryazanov Vladimir
Jazyk: angličtina
Rok vydání: 2016
Předmět:
Zdroj: Open Mathematics, Vol 14, Iss 1, Pp 13-18 (2016)
Druh dokumentu: article
ISSN: 2391-5455
DOI: 10.1515/math-2016-0002
Popis: We proved the existence of multivalent solutions with the infinite number of branches for the Riemann-Hilbert problem in the general settings of finitely connected domains bounded by mutually disjoint Jordan curves, measurable coefficients and measurable boundary data. The theorem is formulated in terms of harmonic measure and principal asymptotic values. It is also given the corresponding reinforced criterion for domains with rectifiable boundaries stated in terms of the natural parameter and nontangential limits. Furthermore, it is shown that the dimension of the spaces of these solutions is infinite.
Databáze: Directory of Open Access Journals