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Elliptic gradient estimates for a nonlinear f-heat equation on weighted manifolds with evolving metrics and potentials

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posted on 2023-06-09, 22:53 authored by Abimbola Abolarinwa, Ali TaheriAli Taheri
We develop local elliptic gradient estimates for a basic nonlinear f-heat equation with a logarithmic power nonlinearity and establish pointwise upper bounds on the weighted heat kernel, all in the context of weighted manifolds, where the metric and potential evolve under a Perelman-Ricci type flow. For the heat bounds use is made of entropy monotonicity arguments and ultracontractivity estimates with the bounds expressed in terms of the optimal constant in the logarithmic Sobolev inequality. Some interesting consequences of these estimates are presented and discussed.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Chaos, Solitons & Fractals

ISSN

0960-0779

Publisher

Elsevier

Volume

142

Page range

1-14

Article number

a110329

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Analysis and Partial Differential Equations Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2021-01-26

First Open Access (FOA) Date

2021-12-08

First Compliant Deposit (FCD) Date

2021-01-26

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