This article is cited in 2 papers

Representation of extremal functions in the classes $E_q$ in terms of Green's and Neumann's functions

S. Ya. Khavinson

Moscow State University of Civil Engineering

Abstract: We consider extremal problems in the classes $E_q$, $q\ge1$, in finitely connected domains and we establish a representation of extremal functions in terms of Green's and Neumann's functions. The equations which we obtain constitute an extension to the multiply connected case of known representation equations for extremal functions in the classes $H_q$ in the unit disk.

UDC: 517.5

Received: 23.06.1972

 English version: Mathematical Notes, 1974, 16:5, 1018–1023

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