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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 2018: 2.316

CiteScore 2018: 1.77

SCImago Journal Rank (SJR) 2018: 2.350
Source Normalized Impact per Paper (SNIP) 2018: 1.465

Mathematical Citation Quotient (MCQ) 2018: 1.44

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Volume 9, Issue 1


The Steiner tree problem revisited through rectifiable G-currents

Andrea Marchese / Annalisa Massaccesi
Published Online: 2014-07-26 | DOI: https://doi.org/10.1515/acv-2014-0022


The Steiner tree problem can be stated in terms of finding a connected set of minimal length containing a given set of finitely many points. We show how to formulate it as a mass-minimization problem for 1-dimensional currents with coefficients in a suitable normed group. The representation used for these currents allows to state a calibration principle for this problem. We also exhibit calibrations in some examples.

Keywords: Steiner tree problem; rectifiable currents; calibration; flat G-chains

MSC: 49Q15; 49Q20

About the article

Received: 2013-04-02

Revised: 2014-04-30

Accepted: 2014-07-09

Published Online: 2014-07-26

Published in Print: 2016-01-01

Citation Information: Advances in Calculus of Variations, Volume 9, Issue 1, Pages 19–39, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv-2014-0022.

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Sergio Conti, Adriana Garroni, and Annalisa Massaccesi
Calculus of Variations and Partial Differential Equations, 2015, Volume 54, Number 2, Page 1847

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