科研之友
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摘要
In this short note, we obtain a "Phi-gradient estimate" for bounded solutions to the heat equation on compact Riemannian manifolds, which generalizes the well-known Hamilton gradient estimate [R.S. Hamilton, A matrix Harnack estimate for the heat equation, Comm. Anal. Geom. 1 (1993) 113-126]. We derive as applications some useful estimates for the Phi-entropy and the associated heat kernel.
