Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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GRADIENT ESTIMATES AND HARNACK INEQUALITES OF NONLINEAR HEAT EQUATIONS FOR THE V -LAPLACIAN

  • Dung, Ha Tuan (Department of Mathematics Hanoi Pedagogical University No. 2)
  • Received : 2017.01.27
  • Accepted : 2018.08.29
  • Published : 2018.11.01
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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.

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References

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