GradEst-ChSoFr2020.pdf (386.48 kB)
Elliptic gradient estimates for a nonlinear f-heat equation on weighted manifolds with evolving metrics and potentials
journal contribution
posted on 2023-06-09, 22:53 authored by Abimbola Abolarinwa, Ali TaheriAli TaheriWe 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.
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Publication status
- Published
File Version
- Accepted version
Journal
Chaos, Solitons & FractalsISSN
0960-0779Publisher
ElsevierExternal DOI
Volume
142Page range
1-14Article number
a110329Department 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
2021-01-26First Open Access (FOA) Date
2021-12-08First Compliant Deposit (FCD) Date
2021-01-26Usage metrics
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