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Bibliographic Details
Main Author: Lu, Zhihao
Format: Preprint
Published: 2023
Subjects:
Online Access:https://arxiv.org/abs/2308.14026
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author Lu, Zhihao
author_facet Lu, Zhihao
contents We derive the complete and optimal Cheng--Yau gradient estimates and universal bounds for subcritical semilinear elliptic equations on Riemannian manifolds with (Bakry-Émery) 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.
format Preprint
id arxiv_https___arxiv_org_abs_2308_14026
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Logarithmic gradient estimate and Universal bounds for semilinear elliptic equations revisited
Lu, Zhihao
Analysis of PDEs
We derive the complete and optimal Cheng--Yau gradient estimates and universal bounds for subcritical semilinear elliptic equations on Riemannian manifolds with (Bakry-Émery) 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.
title Logarithmic gradient estimate and Universal bounds for semilinear elliptic equations revisited
topic Analysis of PDEs
url https://arxiv.org/abs/2308.14026