TY  - JOUR
AU  - Cui, Yanyan
AU  - Wang, Chaojun
PY  - 2024
TI  - The inhomogeneous complex partial differential equations for bi-polyanalytic functions
JO  - AIMS Mathematics
SP  - 16526
EP  - 16543
VL  - 9
IS  - 6
AB  - 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.
UR  - https://doi.org/10.3934/math.2024801
DO  - 10.3934/math.2024801