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Izv. Vyssh. Uchebn. Zaved. Mat., 2012, Number 12, Pages 84–89 (Mi ivm8761)  

Brief communications

Inverse boundary value problems in the Cauchy statement for harmonic functions

N. R. Abubakirova, L. A. Aksent'evb

a Chair of General Mathematics, Kazan (Volga Region) Federal University, Kazan, Russia
b Chair of Mathematical Analysis, Kazan (Volga Region) Federal University, Kazan, Russia

Abstract: 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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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:12, 71–75

Bibliographic databases:

UDC: 517.544
Received: 11.04.2012

Citation: N. R. Abubakirov, L. A. Aksent'ev, “Inverse boundary value problems in the Cauchy statement for harmonic functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 12, 84–89; Russian Math. (Iz. VUZ), 56:12 (2012), 71–75

Citation in format AMSBIB
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\by N.~R.~Abubakirov, L.~A.~Aksent'ev
\paper Inverse boundary value problems in the Cauchy statement for harmonic functions
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2012
\issue 12
\pages 84--89
\mathnet{http://mi.mathnet.ru/ivm8761}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3137112}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2012
\vol 56
\issue 12
\pages 71--75
\crossref{https://doi.org/10.3103/S1066369X12120080}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84872237210}


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  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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