Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exponential bounds for gradient of solutions to linear elliptic and
  parabolic equations   In this paper, we prove global gradient estimates for solutions to linear
elliptic and parabolic equations. For a sufficiently smooth bounded convex
domain $\Omega \subset \mathbb{R}^N$, we show that a solution $\phi \in
W_0^{1,\infty}(\Omega)$ to an appropriate elliptic equation $\mathcal{L} \phi =
F$, with $F \in L^{\infty}(\Omega;\mathbb{R})$, satisfies $|\nabla
\phi|_{\infty} \leq C |F|_{\infty}$, with a positive constant $C =
\exp(C(\mathcal{L})\text{diam}(\Omega))$. We also obtain similiar estimates in
the parabolic setting. The proof of these exponential bounds relies on global
gradient estimates inspired by a series of papers by Ben Andrews and Julie
Clutterbuck. This work is motivated by a dual version of the Landis conjecture.

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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
18
The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
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The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph