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Journal of Siberian Federal University. Mathematics & Physics, 2014, Volume 7, Issue 1, Pages 79–90 (Mi jsfu355)  
An extremal problem related to analytic continuation

Olimjan Makhmudova, Nikolai Tarkhanovb

a Department of Mechanics and Mathematics, University of Samarkand, University Boulevard, 15, 703004, Samarkand, Uzbekistan
b Institute of Mathematics, University of Potsdam, Am Neuen Palais, 10, Potsdam, 14469 Germany
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Abstract: We show that the usual variational formulation of the problem of analytic continuation from an arc on the boundary of a plane domain does not lead to a relaxation of this overdetermined problem. To attain such a relaxation, we bound the domain of the functional, thus changing the Euler equations.
Keywords: extremal problems, Euler equations, $p$-Laplace operator, mixed problems.
Received: 06.07.2013
Received in revised form: 06.09.2013
Accepted: 06.10.2013
Document Type: Article
UDC: 517.55
Language: English
Citation: Olimjan Makhmudov, Nikolai Tarkhanov, “An extremal problem related to analytic continuation”, J. Sib. Fed. Univ. Math. Phys., 7:1 (2014), 79–90
Citation in format AMSBIB
\Bibitem{MakTar14}
\by Olimjan~Makhmudov, Nikolai~Tarkhanov
\paper An extremal problem related to analytic continuation
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2014
\vol 7
\issue 1
\pages 79--90
\mathnet{http://mi.mathnet.ru/jsfu355}
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