A higher-order Riemann-Hilbert problem for inhomogeneous complex partial differential equations
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 $ \mathbb{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.
Fields of Study & Subjects
Differential Equations and Boundary Problems
Analytic and geometric function theory
Holomorphic and Operator Theory
Publication details
- Journal / source
- AIMS Mathematics
- Volume
- 11
- Issue
- 1
- Pages
- 1463–1488
- Publication date
- 1 January 2026