AV Bitsadze's observation on bianalytic functions and the Schwarz problem

Date

2019-08-03

Author

AKSOY, ÜMİT
Begehr, Heinrich
ÇELEBİ, AHMET OKAY

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According to an observation of A.V. Bitsadze from 1948 the Dirichlet problem for bianalytic functions is ill-posed. A natural boundary condition for the polyanalytic operator, however, is the Schwarz condition. An integral representation for the solutions in the unit disc to the inhomogeneous polyanalytic equation satisfying Schwarz boundary conditions is known. This representation is extended here to any simply connected plane domain having a harmonic Green function. Some other boundary value problems are investigated with some Dirichlet and Neumann conditions illuminating that just the Schwarz problem is a natural boundary condition for the Bitsadze operator.

Subject Keywords

Soldatov, Bitsadze equation;, Polyanalytic function, Plane domains, Harmonic Green function, Schwarz boundary value problem, Dirichlet and Neumann conditions

URI

https://hdl.handle.net/11511/66728

Journal

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS

DOI

https://doi.org/10.1080/17476933.2018.1504039

Collections

Department of Mathematics, Article

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Citation Formats

Ü. AKSOY, H. Begehr, and A. O. ÇELEBİ, “AV Bitsadze’s observation on bianalytic functions and the Schwarz problem,” COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, pp. 1257–1274, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/66728.