Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlocal diffusion equations in Carnot Groups   Let $G$ be a Carnot group. We study nonlocal diffusion equations in a domain
$\Omega$ of $G$ of the form $$
u_t^\epsilon(x,t)=\int_{G}\frac{1}{\epsilon^2}K_{\epsilon}(x,y)(u^\epsilon(y,t)-u^\epsilon(x,t))\,dy,
\qquad x\in \Omega $$ with $u^\epsilon=g(x,t)$ for $x\notin\Omega$. For
appropriate rescaled kernel $K_\epsilon$ we prove that solutions $u^\epsilon$,
when $\epsilon\rightarrow0$, uniformly approximate the solution of different
local Dirichlet problem in $G$. The key tool used is the Taylor series
development for a function defined on a Carnot group.

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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex