Some gradient estimates for nonlinear heat-type equations on smooth metric measure spaces with compact boundary

Autor:	Abolarinwa, Abimbola
Rok vydání:	2023
Předmět:	Mathematics - Analysis of PDEs Mathematics - Differential Geometry 35K55 35K58 58J35 58J60 60J60
Druh dokumentu:	Working Paper
Popis:	In this paper we prove some Hamilton type and Li-Yau type gradient estimates on positive solutions to generalized nonlinear parabolic equations on smooth metric measure space with compact boundary. The geometry of the space in terms of lower bounds on the weighted Bakry-Emery Ricci curvature tensor and weighted mean curvature of the boundary are key in proving generalized local and global gradient estimates. Various applications of these gradient estimates in terms of parabolic Harnack inequalities and Liouville type results are discussed. Further consequences to some specific models informed by the nature of the nonlinearities are highlighted. Comment: 46
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.00763 Zobrazit plný text záznamu View this record from Arxiv