Gradient estimates for a nonlinear parabolic equation on smooth metric measure spaces with evolving metrics and potentials
Analysis of PDEs
2023-03-13 v1
Abstract
This article presents new parabolic and elliptic type gradient estimates for positive smooth solutions to a nonlinear parabolic equation involving the Witten Laplacian in the context of smooth metric measure spaces. The metric and potential here are time dependent and evolve under a super Perelman-Ricci flow. The estimates are derived under natural lower bounds on the associated generalised Bakry-\'Emery Ricci curvature tensors and are utilised in establishing fairly general local and global bounds, Harnack-type inequalities and Liouville-type global constancy theorems to mention a few. Other implications and consequences of the results are also discussed.
Keywords
Cite
@article{arxiv.2303.05802,
title = {Gradient estimates for a nonlinear parabolic equation on smooth metric measure spaces with evolving metrics and potentials},
author = {Ali Taheri and Vahideh Vahidifar},
journal= {arXiv preprint arXiv:2303.05802},
year = {2023}
}
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41 pages