On the Riemann-Hilbert problem in multiply connected domains

• Autorzy: Vladimir Ryazanov
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Riemann-Hilbert problem; Multivalent solutions; Multiply connected domains; Jordan curves; Harmonic measures; Principal asymptotic values; Rectifiable boundaries; Natural parameter; Nontangential limits

Kategorie tematyczne

• 35F45: Boundary value problems for linear first-order systems
• 31B25: Boundary behavior
• 31A25: Boundary value and inverse problems
• 35Q15: Riemann-Hilbert problems
• 31A05: Harmonic, subharmonic, superharmonic functions
• 31C05: Harmonic, subharmonic, superharmonic functions
• 30E25: Boundary value problems
• 31A20: Boundary behavior (theorems of Fatou type, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2016
• Tom: 14
• Numer: 1
• Strony: 13-18

Daty

wydano

2016-01-01

otrzymano

2015-09-04

zaakceptowano

2015-12-18

online

2016-02-09

Twórcy

autor

Vladimir Ryazanov

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

Identyfikatory

DOI

10.1515/math-2016-0002