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

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Date

2019

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Taylor & Francis Ltd

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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Abstract

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.

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CELEBI, Ahmet/0000-0002-3508-2590; Aksoy, Umit/0000-0002-6014-1898
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CELEBI, Ahmet ORCID logo
Aksoy, Umit ORCID logo

Keywords

A, Soldatov, Bitsadze equation, polyanalytic function, plane domains, harmonic Green function, Schwarz boundary value problem, Dirichlet and Neumann conditions

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8

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Volume

64

Issue

8

Start Page

1257

End Page

1274

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https://doi.org/10.1080/17476933.2018.1504039
 https://hdl.handle.net/20.500.14411/3281

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