@article{Cui2026, 
author = {Yanyan Cui and Chaojun Wang},
title = {A higher-order Riemann-Hilbert problem for inhomogeneous complex partial differential equations},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {1},
pages = {1463-1488},
keywords = {boundary value problems, Cauchy-Pompeiu formula, Riemann-Hilbert problems, complex partial differential equations, Cauchy-Pompeiu formula},
url = {https://www.sciopen.com/article/10.3934/math.2026062},
doi = {10.3934/math.2026062},
abstract = {In this paper, we mainly discussed an inhomogeneous Riemann-Hilbert boundary value problem for complex partial differential operators of higher order on the bicylinder        D    2   in              C        2  . Applying the classical Cauchy-Pompeiu formula and the Gauss theorem, we found out the solvable condition and obtained the specific solution of the inhomogeneous boundary value problem on the bicylinder        D    2  . The conclusion lays a solid foundation for further research on other types of boundary value problems concerning complex partial differential equations, such as mixed boundary value problems.}
}