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Higher integrability for constrained minimizers of integral functionals with (p, q)-growth in low dimension

Abstract:
We prove higher summability for the gradient of minimizers of strongly convex integral functionals of the Calculus of Variations ˆ Ω f(x, Du(x)) dx, u : Ω ⊂ R n → S N−1 , with growth conditions of (p, q)-type: |ξ| p ≤ f(x, ξ) ≤ C(|ξ| q + 1), p < q, in low dimension. Our procedure is set in the framework of Fractional Sobolev Spaces and renders the desired regularity as the result of an approximation technique relying on estimates obtained through a careful use of difference quotients.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1016/j.na.2017.12.007

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Pembroke College
Role:
Author
ORCID:
0000-0002-3432-1908
Publisher:
Elsevier Publisher's website
Journal:
Nonlinear Analysis Journal website
Volume:
170
Pages:
1-20
Publication date:
2018-01-30
Acceptance date:
2017-12-11
DOI:
ISSN:
0362-546X
Source identifiers:
1005190
Language:
English
Keywords:
Pubs id:
pubs:1005190
UUID:
uuid:368246ff-63f0-434e-bc3c-bae64ec3686c
Local pid:
pubs:1005190
Deposit date:
2019-06-03

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