Hamilton and Li–Yau type gradient estimates for a weighted nonlinear parabolic equation under a super Perelman–Ricci flow

Ali Taheri () and Vahideh Vahidifar ()
Additional contact information
Ali Taheri: University of Sussex
Vahideh Vahidifar: University of Sussex

Partial Differential Equations and Applications, 2024, vol. 5, issue 1, 1-38

Abstract: Abstract In this paper we derive elliptic and parabolic type gradient estimates for positive smooth solutions to a class of nonlinear parabolic equations on smooth metric measure spaces where the metric and potential are time dependent and evolve under a super Perelman–Ricci flow. A number of implications, notably, a parabolic Harnack inequality, a class of Hamilton type dimension-free gradient estimates and two general Liouville type theorems along with their consequences are discussed. Some examples and special cases are presented to illustrate the results.

Keywords: Smooth metric measure spaces; f-Laplacian; Super Perelman–Ricci flow; Gradient estimates; Bakry–Émery tensor; Harnack inequality; Liouville type results; 53C44; 58J60; 58J35; 60J60 (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s42985-023-00269-5 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:pardea:v:5:y:2024:i:1:d:10.1007_s42985-023-00269-5

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/42985/

DOI: 10.1007/s42985-023-00269-5

Access Statistics for this article

Partial Differential Equations and Applications is currently edited by Zhitao Zhang

More articles in Partial Differential Equations and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().