Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global higher integrability for minimisers of convex functionals with
  (p,q)-growth   We prove global $W^{1,q}(\Omega,\mathbb{R}^m)$-regularity for minimisers of
convex functionals of the form $\mathscr{F}(u)=\int_\Omega F(x,Du)\mathrm{d}
x$. $W^{1,q}(\Omega,\mathbb{R}^m)$ regularity is also proven for minimisers of
the associated relaxed functional. Our main assumptions on $F(x,z)$ are a
uniform $\alpha$-H\"older continuity assumption in $x$ and controlled
$(p,q)$-growth conditions in $z$ with $q<\frac{(n+\alpha)p}{n}$.

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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph