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Advances in Calculus of Variations

Managing Editor: Duzaar, Frank / Kinnunen, Juha

Editorial Board Member: Armstrong, Scott N. / Astala, Kari / Colding, Tobias / Dacorogna, Bernard / Dal Maso, Gianni / DiBenedetto, Emmanuele / Fonseca, Irene / Finster, Felix / Gianazza, Ugo / Gursky, Matthew / Hardt, Robert / Ishii, Hitoshi / Kristensen, Jan / Manfredi, Juan / Martell, Jose Maria / McCann, Robert / Mingione, Giuseppe / Nystrom, Kaj / Pacard, Frank / Preiss, David / Riviére, Tristan / Schaetzle, Reiner / Silvestre, Luis

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IMPACT FACTOR 2016: 1.182

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Online
ISSN
1864-8266
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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

Abstract.

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, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv-2012-0004.

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© 2013 by Walter de Gruyter Berlin Boston. Copyright Clearance Center

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