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Article Citation - WoS: 8Citation - Scopus: 9Av Bitsadze's Observation on Bianalytic Functions and the Schwarz Problem Revisited(Taylor & Francis Ltd, 2021) Aksoy, Umit; Begehr, Heinrich; Celebi, A. OkayThe extension of the Schwarz representation formula to simply connected domains with harmonic Green function and its polyanalytic generalization is not valid in general. They do hold only for certain domains.Article Citation - WoS: 10Citation - Scopus: 10Av Bitsadze's Observation on Bianalytic Functions and the Schwarz Problem(Taylor & Francis Ltd, 2019) Aksoy, Umit; Begehr, Heinrich; Celebi, A. OkayAccording 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.Article Citation - WoS: 14Citation - Scopus: 17Schwarz problem for higher-order complex elliptic partial differential equations(Taylor & Francis Ltd, 2008) Aksoy, U.; Celebi, A. O.In this paper, we investigate the solvability of a higher order elliptic differential equation with the Schwarz conditions on the unit disc of the complex plane.
