Harnack estimates for nonlinear heat equations with potentials in geometric flows

Hongxin Guo, Masashi Ishida

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

Let M be a closed Riemannian manifold with a family of Riemannian metrics $${g_{\it ij}(t)}$$gij(t) evolving by geometric flow (Formula Presnted) is a family of smooth symmetric two-tensors on M. In this paper we derive differential Harnack estimates for positive solutions to the nonlinear heat equation with potential: (Formula Presnted) ,where $${\gamma (t)}$$γ(t) is a continuous function on t, a is a constant and (Formula Presnted) is the trace of (Formula Presnted). Our Harnack estimates include many known results as special cases, and moreover lead to new Harnack inequalities for a variety geometric flows.

Original languageEnglish
Pages (from-to)471-484
Number of pages14
Journalmanuscripta mathematica
Volume148
Issue number3-4
DOIs
Publication statusPublished - 2015 Nov 1

Keywords

  • 53C21
  • 53C44

ASJC Scopus subject areas

  • Mathematics(all)

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