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. 
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     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},
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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/

[1] Demidov A. S., Platuschikhin D. A., “Yavnaya formula dlya gradienta garmonicheskoi funktsii po ee analiticheskim dannym Koshi na analiticheskoi krivoi”, Matem. zametki, 87:1 (2010), 141–143 | DOI | MR | Zbl

[2] Demtchenko B., “Sur un probleme inverse au probleme de Dirichlet”, Compt. Rend. Acad. Sci. Paris, 189 (1929), 725–726 | Zbl

[3] Tumashev G. G., Nuzhin M. T., Obratnye kraevye zadachi i ikh prilozheniya, Izd-vo Kazansk. un-ta, Kazan, 1965 | MR

[4] Petrovskii I. A., Lektsii ob uravneniyakh s chastnymi proizvodnymi, Fizmatlit, M., 1961 | MR

[5] Gakhov F. D., Kraevye zadachi, Fizmatlit, M., 1977 | MR | Zbl