Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity for minimizers for functionals of double phase with variable
  exponents   The functionals of double phase type \[ \mathcal{H} (u):= \int \left(|Du|^{p}
+ a(x)|Du|^{q} \right) dx, ( q > p > 1, a(x)\geq 0) \] are introduced in the
epoch-making paper by Colombo-Mingione for constants $p$ and $q$, and
investigated by them and Baroni. They obtained sharp regularity results for
minimizers of such functionals. In this paper we treat the case that the
exponents are functions of $x$ and partly generalize their regularity results.

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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph