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

  • Dung, Ha Tuan
  • Received : 2017.01.27
  • Accepted : 2018.08.29
  • Published : 2018.11.01

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

Acknowledgement

Supported by : Hanoi Pedagogical University No. 2