Logarithmic gradient estimate and Universal bounds for semilinear elliptic equations revisited
Analysis of PDEs
2026-05-05 v2
Abstract
We derive the complete and optimal Cheng--Yau gradient estimates and universal bounds for subcritical semilinear elliptic equations on Riemannian manifolds with (Bakry-\'{E}mery) Ricci curvature bounded below. This answers a fundamental question that has existed for a long time. As a corollary, this provides a new proof of the Gidas-Spruck classical Liouville theorem. The Harnack inequality is also obtained.
Keywords
Cite
@article{arxiv.2308.14026,
title = {Logarithmic gradient estimate and Universal bounds for semilinear elliptic equations revisited},
author = {Zhihao Lu},
journal= {arXiv preprint arXiv:2308.14026},
year = {2026}
}
Comments
This version retains Theorem 1.6 in original version and its proof, and adds several recent related references