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

  • Miroslav Bulíček EMAIL logo , Giovanni Cupini , Bianca Stroffolini and Anna Verde
Published/Copyright: April 19, 2017

Abstract

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.

MSC 2010: 35J47; 35J25

Communicated by Frank Duzaar


Funding statement: 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).

Acknowledgements

We thank the anonymous referee for his/her careful reading of the paper and valuable comments.

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Received: 2016-11-10
Revised: 2017-01-26
Accepted: 2017-03-15
Published Online: 2017-04-19
Published in Print: 2018-07-01

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