Geodesic
Markushevich's ill-posed boundary-value problem for multiply connected domains with circular boundaries
Izvestiya. Mathematics , Tome 76 (2012) no. 6, pp. 1218-1256

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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. 
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     author = {I. Kh. Sabitov},
     title = {Markushevich's ill-posed boundary-value problem for multiply connected domains with circular boundaries},
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I. Kh. Sabitov. Markushevich's ill-posed boundary-value problem for multiply connected domains with circular boundaries. Izvestiya. Mathematics , Tome 76 (2012) no. 6, pp. 1218-1256. http://geodesic.mathdoc.fr/item/IM2_2012_76_6_a8/