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A Sharp Gradient Harnack Estimate for the Lane--Emden System
Abstract
We establish a sharp pointwise gradient estimate for positive entire classical solutions of the Lane--Emden system when one of the exponents lies below the Serrin exponent n/(n−2). The estimate generalizes the positivity of the scalar curvature of the associated conformal metric in the biharmonic case q=1. The coefficient in the estimate is optimal on the critical hyperbola.
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BibTeX
@misc{lee2026sharp,
title = {{A Sharp Gradient Harnack Estimate for the Lane--Emden System}},
author = {Sanghoon Lee and Kui Li and Juncheng Wei},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31584},
eprint = {2610.31584},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31584},
}
RIS
TY - UNPB
TI - A Sharp Gradient Harnack Estimate for the Lane--Emden System
AU - Sanghoon Lee
AU - Kui Li
AU - Juncheng Wei
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31584
UR - https://arxiv.org/abs/2610.31584
AB - We establish a sharp pointwise gradient estimate for positive entire classical solutions of the Lane--Emden system when one of the exponents lies below the Serrin exponent n/(n−2). The estimate generalizes the positivity of the scalar curvature of the associated conformal metric in the biharmonic case q=1. The coefficient in the estimate is optimal on the critical hyperbola.
ER -