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arXiv · 2308.14026

Logarithmic gradient estimate and Universal bounds for semilinear elliptic equations revisited

Zhihao Lu
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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.

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Zhihao Lu. 2023-08-27. Logarithmic gradient estimate and Universal bounds for semilinear elliptic equations revisited. https://arxiv.org/abs/2308.14026

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