Gradient estimates for positive weak solution to $\Delta_pu+au^{\sigma}=0$ on Riemannian manifolds
arXiv (Cornell University)(2023)
摘要
In this paper, we study gradient estimates for positive weak solutions to the following $p$-Laplacian equation $$\Delta_pu+au^{\sigma}=0$$ on a Riemannian manifold, where $p>1$ and $a,\sigma$ are two nonzero real constants. By virtue of the Morser iteration technique, we derive some gradient estimates, which show that when the Ricci curvature is nonnegative, the above equation does not admit positive weak solutions under some scopes of $p$.
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关键词
gradient estimates,riemannian manifolds,positive weak solution
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