On the Riemann-Hilbert problem in multiply connected domains

Open Mathematics

Ryazanov Vladimir¹ 

[1] Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, 1 Dobrovolskii Str., 84100, Slavyansk, Ukraine;

关键词: riemann-hilbert problem;    multivalent solutions;    multiply connected domains;    jordan curves;    harmonic measures;    principal asymptotic values;    rectifiable boundaries;    natural parameter;    nontangential limits;    31a05;    31a20;    31a25;    31b25;    35q15;    30e25;    31c05;    35f45;   

DOI  :  10.1515/math-2016-0002

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown