Higher integrability for variational integrals with non-standard growth

We consider autonomous integral functionals of the form F [ u ] : = ∫ Ω f ( D u ) d x where u : Ω → R N , N ≥ 1 , where the convex integrand f satisfies controlled ( p ,  q )-growth conditions. We establish higher gradient integrability and partial regularity for minimizers of F assuming q p < 1...

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2021-04, Vol.60 (2), Article 77
Main Author: Schäffner, Mathias
Format: Article
Language:English
Subjects:
Analysis
Calculus of Variations and Optimal Control
Optimization
Control
Integral calculus
Integrals
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Systems Theory
Theoretical
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Summary:We consider autonomous integral functionals of the form F [ u ] : = ∫ Ω f ( D u ) d x where u : Ω → R N , N ≥ 1 , where the convex integrand f satisfies controlled ( p ,  q )-growth conditions. We establish higher gradient integrability and partial regularity for minimizers of F assuming q p < 1 + 2 n - 1 , n ≥ 3 . This improves earlier results valid under the more restrictive assumption q p < 1 + 2 n .
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-020-01907-1