Elliptic gradient estimates for the doubly nonlinear diffusion equation. (November 2018)

• Record Type: Journal Article
• Authors: Yan, Shan; Wang, Lin Feng
• Is Part Of: Nonlinear analysis. Volume 176(2018)
• Page Start: 20
• Page End: 35
• Publication Date: 2018-11
• Subjects: 53C21; Doubly nonlinear diffusion equation -- Fast diffusion equation -- p-Laplace parabolic equation -- Gradient estimate -- Harnack inequality; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2018.06.004
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we establish elliptic type gradient estimates for positive solutions to the doubly nonlinear diffusion equation on compact or complete noncompact Riemannian manifolds. As special cases, we can derive elliptic type gradient estimates for positive solutions to the p -Laplace parabolic equations and the fast diffusion equations. Harnack inequalities derived from these elliptic type gradient estimates can be used to compare solutions at the same time.