Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local boundedness and Harnack inequality for solutions of linear
  non-uniformly elliptic equations   We study local regularity properties for solutions of linear, non-uniformly
elliptic equations. Assuming certain integrability conditions on the
coefficient field, we prove local boundedness and Harnack inequality. The
assumed integrability assumptions are essentially sharp and improve upon
classical results by Trudinger [ARMA 1971]. We then apply the deterministic
regularity results to the corrector equation in stochastic homogenization and
establish sublinearity of the corrector.

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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
4
The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc