Geodesic
An extremal problem related to analytic continuation
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 7 (2014) no. 1, pp. 79-90

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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, $p$-Laplace operator, mixed problems.
Mots-clés : Euler equations 
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Olimjan Makhmudov; Nikolai Tarkhanov. An extremal problem related to analytic continuation. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 7 (2014) no. 1, pp. 79-90. http://geodesic.mathdoc.fr/item/JSFU_2014_7_1_a7/