[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j170083

GRADIENT ESTIMATES AND HARNACK INEQUALITES OF NONLINEAR HEAT EQUATIONS FOR THE V -LAPLACIAN

Dung, Ha Tuan (Department of Mathematics Hanoi Pedagogical University No. 2)

Publication Information

Journal of the Korean Mathematical Society / v.55, no.6, 2018 , pp. 1285-1303 More about this Journal

Abstract

This note is motivated by gradient estimates of Li-Yau, Hamilton, and Souplet-Zhang for heat equations. In this paper, our aim is to investigate Yamabe equations and a non linear heat equation arising from gradient Ricci soliton. We will apply Bochner technique and maximal principle to derive gradient estimates of the general non-linear heat equation on Riemannian manifolds. As their consequence, we give several applications to study heat equation and Yamabe equation such as Harnack type inequalities, gradient estimates, Liouville type results.

Keywords

gradient estimates; Bakry- ${\acute{E}}mery$ curvature; Bochner's technique; Harnack-type inequalities; Liouville-type theorems;

Citations & Related Records

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