Abimbola Abolarinwa
Abstract:
Let (M,g) be an n dimensional complete Riemannian manifold.
In this article we prove local Li-Yau type gradient estimates for all positive
solutions to the nonlinear parabolic equation
along the generalised geometric flow on M. Here
is a smooth potential function and a
is an arbitrary constant. As an application we derive a global estimate and
a space-time Harnack inequality.
Submitted December 8, 2014. Published January 8, 2015.
Math Subject Classifications: 35K55, 53C21, 53C44, 58J35.
Key Words: Gradient estimates; Harnack inequalities; parabolic equations;
geometric flows.
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Abimbola Abolarinwa Department of Mathematics, University of Sussex Brighton, BN1 9QH, United Kingdom email: A.Abolarinwa@sussex.ac.uk |
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