Gradient estimates for a nonlinear parabolic equation on complete non-compact Riemannian manifolds |
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Authors: | Li Chen Wenyi Chen |
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Affiliation: | (1) School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, People’s Republic of China |
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Abstract: | In this paper, we derive a local gradient estimate for the positive solution to the following parabolic equation , where a, b are real constants, M is a complete noncompact Riemannian manifold. As a corollary, we give a local gradient estimate for the corresponding elliptic equation: , which improves and extends the result of Ma (J Funct Anal 241:374–382, 2006) and get a bound for the positive solution to this elliptic equation. |
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Keywords: | Nonlinear parabolic equation Gradient estimate Positive solution |
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