Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity of the extremal solution for some elliptic problems with
  advection   In this note, we investigate the regularity of extremal solution $u^*$ for
semilinear elliptic equation $-\triangle u+c(x)\cdot\nabla u=\lambda f(u)$ on a
bounded smooth domain of $\mathbb{R}^n$ with Dirichlet boundary condition. Here
$f$ is a positive nondecreasing convex function, exploding at a finite value
$a\in (0, \infty)$. We show that the extremal solution is regular in low
dimensional case. In particular, we prove that for the radial case, all
extremal solution is regular in dimension two.

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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
1
The categories of this paper are: cs
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The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio