Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A nonlinear elliptic problem involving the gradient on a half space   We consider perturbations of the diffusive Hamilton-Jacobi equation
\begin{equation*} %\label{non_pert}
  \left\{ \begin{array}{lcl} \hfill -\Delta u &=& (1+g(x))| \nabla u|^p\qquad
\mbox{ in } \IR^N_+, \\ \hfill u &=& 0 \hfill \mbox{ on } \partial \IR^N_+,
\end{array}\right.
  \end{equation*}
  for $ p>1$. We prove the existence of a classical solution provided $ p \in
(\frac{4}{3},2)$ and $g$ is bounded with uniform radial decay to zero.

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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom