Jump to ContentJump to Main Navigation
Show Summary Details
More options …

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

4 Issues per year

IMPACT FACTOR 2016: 1.182

CiteScore 2017: 1.30

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

Mathematical Citation Quotient (MCQ) 2016: 0.83

See all formats and pricing
More options …
Volume 6, Issue 4


Regularity versus singularity for elliptic problems in two dimensions

Lisa Beck
Published Online: 2012-08-09 | DOI: https://doi.org/10.1515/acv-2012-0004


In two dimensions every solution to a nonlinear elliptic system

has Hölder continuous first derivatives provided that standard continuity, ellipticity and p-growth assumptions hold for some . We give an example showing that this result cannot be extended to elliptic systems in the subquadratic case, i.e. that weak solutions are not necessarily continuous if . Furthermore, we discuss related results for variational integrals.

Keywords: Quasi-linear elliptic systems; regularity of weak solutions; counterexample in two dimensions

About the article

Received: 2012-04-20

Accepted: 2012-07-12

Published Online: 2012-08-09

Published in Print: 2013-10-01

Citation Information: Advances in Calculus of Variations, Volume 6, Issue 4, Pages 415–432, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv-2012-0004.

Export Citation

© 2013 by Walter de Gruyter Berlin Boston.Get Permission

Comments (0)

Please log in or register to comment.
Log in