On the Riemann-Hilbert problem in multiply connected domains

Vladimir 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 -