TY  - JOUR
T1  - Schwarz Problem for Model Partial Differential Equations with One Complex Variable
AU  - Karaca, Bahriye
PY  - 2024
DA  - April
Y2  - 2024
DO  - 10.16984/saufenbilder.1390617
JF  - Sakarya University Journal of Science
JO  - SAUJS
PB  - Sakarya University
WT  - DergiPark
SN  - 2147-835X
SP  - 410
EP  - 417
VL  - 28
IS  - 2
LA  - en
AB  - This paper investigates the Schwarz problem. Initially, the focus lies on analyzing the problem for the first, second orders. Subsequently, attention shifts towards studying the same problem for equations of higher order. In the realm of second-order equations, the Schwarz problem is specifically examined for some operators; Laplace, Bitsadze and its complex conjugate. The findings demonstrate that the Schwarz problem for an n-order equation, when equipped with solely one boundary condition, exhibits an infinite number of solutions. However, by incorporating additional boundary conditions, it becomes feasible to obtain a unique solution for problem concerning n-order equations, effectively rendering it a well-posed problem.
KW  - Schwarz Problem
KW  - Complex model homogeneous partial differential equation
KW  - Complex model inhomogeneous partial differential equations
CR  - [1]	H. Begehr, “Boundary Value Problems in Complex Analysis Ⅰ, Ⅱ,” Boletin de la Asosiacion, vol. Ⅻ, no. 2, pp. 65-85, 217-250, 2005.
CR  - [2]	 B.  Karaca, “Dirichlet Problem for Complex    Model Partial Differential Equations,” Complex Variables and Elliptic Equations, vol. 65, no. 10, pp. 1748-1762, 2020.
CR  - [3]	H. Begehr, S. Burgumbayeva, B. Shupeyeva, “Harmonic Green Functions for a Plane Domain With Two Touching Circles As Boundary,” Advanced Mathematical Models & Applications, vol. 3, no. 1, pp. 18-29, 2018.
CR  - [4]	Ü. Aksoy, AO.  Çelebi, “Schwarz Problem for Higher Order Linear Equations in a Polydisc,” Complex Variables and Elliptic Equations, vol. 62, no. 10, pp. 1558-1569, 2017.
CR  - [5]	M. Akel, M. Hidan, M. Abdalla, “Complex Boundary Value Problems for the Cauchy–Riemann Operator on a Triangle,” Fractals, vol. 30, no. 10, pp. 1-15, 2022.
CR  - [6]	M. Akel, H. Begehr, A. Mohammed, “A Neumann Problem for the Polyanalytic Operator in Planar Domains with Harmonic Green Function,” Applicable Analysis, vol. 101, no. 11, pp. 3816-3824, 2022.
CR  - [7]	H. Begehr, S. Burgumbayeva, A. Dauletkulova, H. Lin, “Harmonic Green Functions for the Almaty Apple,” Complex Variables and Elliptic Equations, vol. 65, no. 11, pp. 1814-1825, 2020.
CR  - [8]	Ü. Aksoy, H. Begehr, AO. Çelebi, “Schwarz Problem for Higher‐Order Complex Partial Differential Equations in the Upper Half Plane,” Mathematische Nachrichten, vol. 292, no. 6, pp. 1183-1193, 2019.
UR  - https://doi.org/10.16984/saufenbilder.1390617
L1  - https://dergipark.org.tr/en/download/article-file/3536594
ER  -