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

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

2009-07-09

arxiv.org/abs/0907.1440v1

Mathematics

Differential Geometry

6 pages

Scientific paper

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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