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| Paper IPM / M / 17138 |
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| Abstract: | |
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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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