N. R. Abubakirov, L. A. Aksent'ev, “Explicit forms of the Schwarz integral and their application in inverse boundary-value problems”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, Number 10,Pages <nobr>55

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Brief communications

Explicit forms of the Schwarz integral and their application in inverse boundary-value problems

N. R. Abubakirov^a, L. A. Aksent'ev^b

^a Chair of General Mathematics, Kazan (Volga Region) Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia
^b Chair of Mathematical Analysis, Kazan (Volga Region) Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia

Abstract: We obtain new explicit forms of the Schwarz integral in the unit circle. With the help of superpositions of logarithms we establish criteria that characterize the appearance of singular points on the boundary in inverse boundary value problems, as well as criteria for the appearance of boundary circles.

Keywords: Schwarz integral, inverse boundary-value problems, modulus of continuity.

UDC: 517.544

Received: 28.02.2013