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Advances in Calculus of Variations

Managing Editor: Duzaar, Frank / Kinnunen, Juha

Editorial Board: Armstrong, Scott N. / Balogh, Zoltán / Cardiliaguet, Pierre / Dacorogna, Bernard / Dal Maso, Gianni / DiBenedetto, Emmanuele / Fonseca, Irene / Gianazza, Ugo / Ishii, Hitoshi / Kristensen, Jan / Manfredi, Juan / Martell, Jose Maria / Mingione, Giuseppe / Nystrom, Kaj / Riviére, Tristan / Schaetzle, Reiner / Shen, Zhongwei / Silvestre, Luis / Tonegawa, Yoshihiro / Touzi, Nizar / Wang, Guofang

IMPACT FACTOR 2017: 1.676

CiteScore 2017: 1.30

SCImago Journal Rank (SJR) 2017: 2.045
Source Normalized Impact per Paper (SNIP) 2017: 1.138

Mathematical Citation Quotient (MCQ) 2017: 1.15

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Volume 7, Issue 3


Blow-up analysis of stationary two-valued functions

Philippe Bouafia
Published Online: 2013-06-18 | DOI: https://doi.org/10.1515/acv-2012-0021


We consider two-valued real functions of two variables which are stationary with respect to both domain and range transformations. We prove their local Lipschitz continuity and use it to establish strong convergence in W1,2 to their unique blow-up at any point. The main theorem of this paper states that the branch set of any such function consists of finitely many real analytic curves meeting at nod points with equal angles. We also provide an example showing that stationarity with respect to domain transformations only does not imply continuity.

Keywords: Multiple-valued function; stationarity; branching

MSC: 54C60; 49J53

About the article

Received: 2012-09-03

Revised: 2013-02-04

Accepted: 2013-02-09

Published Online: 2013-06-18

Published in Print: 2014-07-01

Citation Information: Advances in Calculus of Variations, Volume 7, Issue 3, Pages 297–326, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv-2012-0021.

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