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A nonlinear elliptic problem involving the gradient on a half space

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A. Aghajani, C. Cowan, S.H. Lui

Analysis of PDEs · Submitted 12 Apr 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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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arXiv ID2104.05205 (version 1)
Pith IDMIVBWXWV, Pith's permanent record of this paper and its review
CitationA. Aghajani, C. Cowan, S.H. Lui. "A nonlinear elliptic problem involving the gradient on a half space." arXiv:2104.05205 (2021). https://pith.science/paper/MIVBWXWV
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,145 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.82 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.89 · compares with prior results 0.06 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 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. background 0.71 0.62 0.04 asserted 0.60
s1 \end{equation*} for $ p>1$. background 0.92 0.11 0.03 unclear 0.77
s2 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. result 0.92 0.96 0.92 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original 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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