@article{Cui2024, 
author = {Yanyan Cui and Chaojun Wang},
title = {The inhomogeneous complex partial differential equations for bi-polyanalytic functions},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {6},
pages = {16526-16543},
keywords = {Riemann-Hilbert problems, complex partial differential equations, Cauchy-Pompeiu formula, bi-polyanalytic functions, Dirichlet problems},
url = {https://www.sciopen.com/article/10.3934/math.2024801},
doi = {10.3934/math.2024801},
abstract = {In this paper, we study a Riemann-Hilbert problem related to inhomogeneous complex partial differential operators of higher order on the unit disk. Applying the Cauchy-Pompeiu formula, we find out the solvable conditions and obtain the representation of the solutions. Then, we investigate the boundary value problems for bi-polyanalytic functions with the Dirichlet and Riemann-Hilbert boundary conditions, obtain the specific solution and the solvable conditions, and extend the conclusion to the corresponding higher-order problems. Therefore, we obtain the solution to the half-Neumann problem of higher order for bi-polyanalytic functions.}
}