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GENERALIZED LI-YAU ESTIMATES AND HUISKEN'S MONOTONICITY FORMULA.
- Source :
-
ESAIM: Control, Optimisation & Calculus of Variations . Jul2017, Vol. 23 Issue 3, p827-850. 24p. - Publication Year :
- 2017
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 12928119
- Volume :
- 23
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- ESAIM: Control, Optimisation & Calculus of Variations
- Publication Type :
- Academic Journal
- Accession number :
- 123147250
- Full Text :
- https://doi.org/10.1051/cocv/2016015