Schwarz problem for higher-order complex partial differential equations in the upper half plane

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Date

2019

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Wiley-v C H verlag Gmbh

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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

Linear and nonlinear elliptic complex partial differential equations of higher-order are considered under Schwarz conditions in the upper-half plane, Firstly, using the integral representations for the solutions of the inhomogeneous polyanalytic equation with Schvvarz conditions, a class of integral operators is introduced together with some of their properties. Then, these operators are used to transform the problem for linear equations into singular integral equations. In the case of nonlinear equations such a transformation yields a system of integro-differential equations. Existence of the solutions of the relevant boundary value problems for linear and nonlinear equations are discussed via Fredholm theory and fixed point theorems, respectively.

Description

Çelebi, Ahmet/0000-0002-3508-2590; Aksoy, Umit/0000-0002-6014-1898

Keywords

complex partial differential equation, polyanalytic, Schwarz problem, upper half plane

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Citation

6

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Q2

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Q2

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Volume

292

Issue

6

Start Page

1183

End Page

1193

URI

https://doi.org/10.1002/mana.201800028
 https://hdl.handle.net/20.500.14411/3378

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