Geodesic
Inverse boundary value problems in the Cauchy statement for harmonic functions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2012), pp. 84-89

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We study the inverse boundary value problem (problem (A)) in the Cauchy statement for an analytic function with unknown curve $\Gamma$. We solve the considered problem by two different methods. We obtain necessary and sufficient conditions for $\Gamma$ to be the unit circumference. With the help of the described methods we solve a modified Hadamard example. We give a generalization for the case of a doubly connected domain.
Keywords: boundary value problems for analytic functions, Cauchy problem, inverse boundary value problems, harmonic functions. 
@article{IVM_2012_12_a7,
     author = {N. R. Abubakirov and L. A. Aksent'ev},
     title = {Inverse boundary value problems in the {Cauchy} statement for harmonic functions},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {84--89},
     publisher = {mathdoc},
     number = {12},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_12_a7/}
}
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N. R. Abubakirov; L. A. Aksent'ev. Inverse boundary value problems in the Cauchy statement for harmonic functions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2012), pp. 84-89. http://geodesic.mathdoc.fr/item/IVM_2012_12_a7/