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arXiv · 2311.01381

Li-Yau Inequality and Liouville Property to a Semilinear Heat Equation on Riemannian Manifolds

Huan-Jie Chen·Shi-Zhong Du·Yue-Xiao Ma
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Abstract

This work deals with the Entire solutions of a nonlinear equation. The first part of this paper is devoted to investigation of the Liouville property on compact manifolds, which extends a result by Castorina-Mantegazza [4] for positive f. Secondly, we will turn to non-compact manifolds and prove a Liouville theorem under the assumptions of boundedness of the Ricci curvature from below, diffeomorphism of M with R^N and sub-criticality of p defined below. Finally, we also present simplified proofs of Yau's theorem for harmonic function and Gidas-Spruck's theorem for elliptic semilinear equation. Our proofs are based on Li-Yau type estimation for nonlinear equations.

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Huan-Jie Chen, Shi-Zhong Du, Yue-Xiao Ma. 2023-11-02. Li-Yau Inequality and Liouville Property to a Semilinear Heat Equation on Riemannian Manifolds. https://arxiv.org/abs/2311.01381

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