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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

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Volume 7, Issue 2


Plateau's problem for integral currents in locally non-compact metric spaces

Stefan Wenger
Published Online: 2013-01-04 | DOI: https://doi.org/10.1515/acv-2012-0018


The purpose of this article is to prove existence of mass minimizing integral currents with prescribed possibly non-compact boundary in all dual Banach spaces and furthermore in certain spaces without linear structure, such as injective metric spaces and Hadamard spaces. We furthermore prove a weak*-compactness theorem for integral currents in dual spaces of separable Banach spaces. Our theorems generalize results of Ambrosio–Kirchheim, Lang, the author, and recent results of Ambrosio–Schmidt.

Keywords: Plateau's problem; area minimizers; Banach spaces; compactness

MSC: 49Q15; 49Q05; 46B50; 53C23

About the article

Received: 2012-07-23

Revised: 2012-11-15

Accepted: 2012-11-28

Published Online: 2013-01-04

Published in Print: 2014-04-01

Funding Source: NSF

Award identifier / Grant number: DMS 0956374

Funding Source: NSF

Award identifier / Grant number: DMS 1056263

Citation Information: Advances in Calculus of Variations, Volume 7, Issue 2, Pages 227–240, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv-2012-0018.

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