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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2020, Volume 188, Pages 54–69
DOI: https://doi.org/10.36535/0233-6723-2020-188-54-69 (Mi into740) 		 
Complex partial differential equations

\. Aksoya, H. Begehrb, A. \c{C}elebic, B. Shupeyevad

a Atilim University, Department of Mathematics
b Freie Universität Berlin, Institut für Mathematik
c Yeditepe University
d Nazarbayev University Research and Innovation System
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DOI: https://doi.org/10.36535/0233-6723-2020-188-54-69
Abstract: The Schwarz and iterated Dirichlet boundary-value problems are reported on for the polyanalytic operator in certain plane domains having a harmonic Green function. Hybrid polyharmonic Green functions are reviewed upon which open a variety of boundary-value problems for the polyharmonic operator. This topic is far from being complete. The higher the order of the polyharmonic operator the richer is the theory of related hybrid Green functions: they are constructed by continued convoluting harmonic Green, Neumann, Robin functions also incorporating polyharmonic Green–Almansi functions.
Keywords: polyanalytic operator, Cauchy–Schwarz–Pompeiu representation, Green function, Schwarz boundary-value problem, Dirichlet boundary-value problem, admissible domain, ring domain, Green–Almansi function, polyharmonic hybrid Green function, polyharmonic boundary-value problem, Riquier boundary-value problem.
Document Type: Article
UDC: 517.95
MSC: 30E25, 30G20, 31A10, 31A25, 35J40
Language: Russian
Citation: \. Aksoy, H. Begehr, A. Çelebi, B. Shupeyeva, “Complex partial differential equations”, Differential Equations and Mathematical Modeling, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 188, VINITI, Moscow, 2020, 54–69
Citation in format AMSBIB
\Bibitem{AksBeg\c{20}
\by \.~Aksoy, H.~Begehr, A.~\c{C}elebi, B.~Shupeyeva
\paper Complex partial differential equations
\inbook Differential Equations and Mathematical Modeling
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2020
\vol 188
\pages 54--69
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into740}
\crossref{https://doi.org/10.36535/0233-6723-2020-188-54-69}
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