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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 6, Issue 2


Energy quantization for biharmonic maps

Paul Laurain / Tristan Rivière
Published Online: 2013-04-01 | DOI: https://doi.org/10.1515/acv-2012-0105


In the present work we establish an energy quantization (or energy identity) result for solutions to scaling invariant variational problems in dimension 4 which includes biharmonic maps (extrinsic and intrinsic). To that end we first establish an angular energy quantization for solutions to critical linear 4th order elliptic systems with antisymmetric potentials. The method is inspired by the one introduced by the authors previously in “Angular energy quantization for linear elliptic systems with antisymmetric potentials and applications” (2011) for 2nd order problems.

Keywords: Fourth order elliptic systems; harmonic maps; conservation laws

About the article

Received: 2012-01-12

Revised: 2012-06-11

Accepted: 2012-06-25

Published Online: 2013-04-01

Published in Print: 2013-04-01

Citation Information: Advances in Calculus of Variations, Volume 6, Issue 2, Pages 191–216, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv-2012-0105.

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