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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 11, Issue 3


Existence and regularity results for weak solutions to (p,q)-elliptic systems in divergence form

Miroslav Bulíček
  • Corresponding author
  • Mathematical Institute, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75, Prague, Czech Republic
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/ Giovanni Cupini / Bianca Stroffolini
  • Dipartimento di Matematica e Applicazioni, Università di Napoli “Federico II”, Via Cintia,80126 Napoli, Italy
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/ Anna Verde
  • Dipartimento di Matematica e Applicazioni, Università di Napoli “Federico II”, Via Cintia,80126 Napoli, Italy
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Published Online: 2017-04-19 | DOI: https://doi.org/10.1515/acv-2016-0054


We prove existence and regularity results for weak solutions of non-linear elliptic systems with non-variational structure satisfying (p,q)-growth conditions. In particular, we are able to prove higher differentiability results under a dimension-free gap between p and q.

Keywords: Elliptic system; existence of solutions; regularity

MSC 2010: 35J47; 35J25


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About the article

Received: 2016-11-10

Revised: 2017-01-26

Accepted: 2017-03-15

Published Online: 2017-04-19

Published in Print: 2018-07-01

Miroslav Bulíček’s work was supported by the ERC-CZ project LL1202 financed by the Ministry of Education, Youth and Sports, Czech Republic. Miroslav Bulíček is a member of the Nečas center for Mathematical Modeling. The other authors are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

Citation Information: Advances in Calculus of Variations, Volume 11, Issue 3, Pages 273–288, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv-2016-0054.

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