# On the Riemann-Hilbert problem in multiply connected domains

Open Mathematics (2016)

- Volume: 14, Issue: 1, page 13-18
- ISSN: 2391-5455

## Access Full Article

top## Abstract

top## How to cite

topVladimir Ryazanov. "On the Riemann-Hilbert problem in multiply connected domains." Open Mathematics 14.1 (2016): 13-18. <http://eudml.org/doc/276888>.

@article{VladimirRyazanov2016,

abstract = {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.},

author = {Vladimir Ryazanov},

journal = {Open Mathematics},

keywords = {Riemann-Hilbert problem; Multivalent solutions; Multiply connected domains; Jordan curves; Harmonic measures; Principal asymptotic values; Rectifiable boundaries; Natural parameter; Nontangential limits; multiply connected domains; harmonic functions},

language = {eng},

number = {1},

pages = {13-18},

title = {On the Riemann-Hilbert problem in multiply connected domains},

url = {http://eudml.org/doc/276888},

volume = {14},

year = {2016},

}

TY - JOUR

AU - Vladimir Ryazanov

TI - On the Riemann-Hilbert problem in multiply connected domains

JO - Open Mathematics

PY - 2016

VL - 14

IS - 1

SP - 13

EP - 18

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/276888

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.