An extremal problem related to analytic continuation

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.

Metadaten
Author details:	Olimdjan Makhmudov, Nikolai Nikolaevich Tarkhanov ORCiD GND
URN:	urn:nbn:de:kobv:517-opus-63634
Publication series (Volume number):	Preprints des Instituts für Mathematik der Universität Potsdam (2 (2013) 4)
Publication type:	Preprint
Language:	English
Publication year:	2013
Publishing institution:	Universität Potsdam
Release date:	2013/02/01
Tag:	Euler equations; Extremal problem; mixed problems; p-Laplace operator
Organizational units:	Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC classification:	5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC classification:	30-XX FUNCTIONS OF A COMPLEX VARIABLE (For analysis on manifolds, see 58-XX) / 30Cxx Geometric function theory / 30C70 Extremal problems for conformal and quasiconformal mappings, variational methods
	35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J50 Variational methods for elliptic systems
	35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J92 Quasilinear elliptic equations with p-Laplacian
Collection(s):	Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2013
License (German):	Keine öffentliche Lizenz: Unter Urheberrechtsschutz
External remark:	RVK-Klassifikation: SI 990