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arXiv · 2104.05205

A nonlinear elliptic problem involving the gradient on a half space

A. Aghajani·C. Cowan·S. H. Lui
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Abstract

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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A. Aghajani, C. Cowan, S. H. Lui. 2021-04-12. A nonlinear elliptic problem involving the gradient on a half space. https://arxiv.org/abs/2104.05205

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