Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Elliptic systems with measurable coefficients of the type of Lam\'e
  system in three dimensions   We study the $3 \times 3$ elliptic systems $\nabla \times (a(x) \nabla\times
u)-\nabla (b(x) \nabla \cdot u)=f$, where the coefficients $a(x)$ and $b(x)$
are positive scalar functions that are measurable and bounded away from zero
and infinity. We prove that weak solutions of the above system are H\"older
continuous under some minimal conditions on the inhomogeneous term $f$. We also
present some applications and discuss several related topics including
estimates of the Green's functions and the heat kernels of the above systems.

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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: econ