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• W2962874434 abstract "We prove a generalization of the Li−Yau estimate for a broad class of second order linear parabolic equations. As a consequence, we obtain a new Cheeger−Yau inequality and a new Harnack inequality for these equations. We also prove a Hamilton−Li−Yau estimate, which is a matrix version of the Li−Yau estimate, for these equations. This results in a generalization of Huisken’s monotonicity formula for a family of evolving hypersurfaces. Finally, we also show that all these generalizations are sharp in the sense that the inequalities become equality for a family of fundamental solutions, which however different from the Gaussian heat kernels on which the equality was achieved in the classical case." @default.
• W2962874434 created "2019-07-30" @default.
• W2962874434 creator A5015679315 @default.
• W2962874434 date "2017-04-10" @default.
• W2962874434 modified "2023-09-27" @default.
• W2962874434 title "Generalized Li−Yau estimates and Huisken’s monotonicity formula" @default.
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• W2962874434 doi "https://doi.org/10.1051/cocv/2016015" @default.
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