Gradient estimate for the Poisson equation and the non-homogeneous heat equation on compact Riemannian manifolds
classification
🧮 math.DG
math.AP
keywords
equationestimategradientheatpositivecompactnon-homogeneouspoisson
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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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