@article{Wang2026, 
author = {Chaojun Wang and Yanyan Cui},
title = {Several boundary value problems arising from the extensions of analytic functions},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {5},
pages = {13660-13682},
keywords = {complex partial differential equations, Hilbert problems, Riemann problems, analytic functions, Cauchy type integral},
url = {https://www.sciopen.com/article/10.3934/math.2026563},
doi = {10.3934/math.2026563},
abstract = {In this paper, with the properties of    β-Cauchy type integrals and the Plemelj formula for the corresponding singular integrals, the Hilbert boundary value problems for    β-analytic functions were first discussed on the unit disc in        C  , and the concrete representations of the solutions were obtained. Thereafter, on the basis of the results for the Riemann boundary value problems for analytic functions, several Riemann problems for higher-order complex partial differential systems and    (  λ  ,  1  ) bi-analytic functions were investigated for the bicylinder in              C        2  . The solutions to the problems and the corresponding solvable conditions were obtained.}
}