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arXiv · 0907.1440

Gradient estimate for the Poisson equation and the non-homogeneous heat equation on compact Riemannian manifolds

Li Ma·Liang Cheng
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Abstract

In this short note, we study the gradient estimate of positive solutions to Poisson equation and the non-homogeneous heat equation in a compact Riemannian manifold (M^n,g). Our results extend the gradient estimate for positive harmonic functions and positive solutions to heat equations.

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Li Ma, Liang Cheng. 2009-07-09. Gradient estimate for the Poisson equation and the non-homogeneous heat equation on compact Riemannian manifolds. https://arxiv.org/abs/0907.1440

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