Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp regularity for general Poisson equations with borderline sources   This article concerns optimal estimates for non-homogeneous degenerate
elliptic equation with source functions in borderline spaces of integrability.
We deliver sharp H\"older continuity estimates for solutions to $p$-degenerate
elliptic equations in rough media with sources in the weak Lebesgue space
$L_\text{weak}^{\frac{n}{p} + \epsilon}$. For the borderline case, $f \in
L_\text{weak}^{\frac{n}{p}}$, solutions may not be bounded; nevertheless we
show that solutions have bounded mean oscillation, in particular
John-Nirenberg's exponential integrability estimates can be employed. All the
results presented in this paper are optimal. Our approach is based on powerful
Caffarelli-type compactness methods and it can be employed in a number order
situations.

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The categories of this paper are: bayes-an
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The categories of this paper are: cs
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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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: q-alg