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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)
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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
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2012, Volume 76, Issue 6, Pages 153–192
DOI: https://doi.org/10.4213/im7798
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. RAN. Ser. Mat., 76:6 (2012), 153–192; Izv. Math., 76:6 (2012), 1218–1256
Citation in format AMSBIB
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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:
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Russian version PDF:219
    English version PDF:21
    References:71
    First page:18
     
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