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Izvestiya: Mathematics, 2012, Volume 76, Issue 6, Pages 1218–1256
DOI: https://doi.org/10.1070/IM2012v076n06ABEH002622 (Mi im7798) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Markushevich's ill-posed boundary-value problem for multiply connected domains with circular boundaries

I. Kh. Sabitov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (502 kB) Citations (2) Russian version article
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DOI: https://doi.org/10.1070/IM2012v076n06ABEH002622
Abstract: We consider a little-known boundary-value problem of linear conjugation in the theory of functions of a complex variable in multiply connected domains. Although it was posed in a general form by Markushevich in 1946 and used in Vekua's geometric studies, it is still poorly understood. The problem is ill-posed: it loses solubility after arbitrarily small perturbations of the coefficient. Under certain simple conditions, we solve the problem completely by establishing necessary and sufficient criteria for its solubility and giving a construction for its solutions.
Keywords: holomorphic and meromorphic functions, linear conjugation problem, ill-posedness of a problem, index, solubility conditions.
Received: 25.05.2011
Revised: 22.12.2011
Bibliographic databases:
Document Type: Article
UDC: 517.53
MSC: 30E25, 53A05
Language: English
Original paper language: Russian
Citation: I. Kh. Sabitov, “Markushevich's ill-posed boundary-value problem for multiply connected domains with circular boundaries”, Izv. Math., 76:6 (2012), 1218–1256
Citation in format AMSBIB
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\paper Markushevich's ill-posed boundary-value problem for multiply connected domains with circular boundaries
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\yr 2012
\vol 76
\issue 6
\pages 1218--1256
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  • https://doi.org/10.1070/IM2012v076n06ABEH002622
  • https://www.mathnet.ru/eng/im/v76/i6/p153
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
     
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