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Journal of the Korean Mathematical Society = 대한수학회지 v.55 no.6, 2018년, pp.1285 - 1303   SCIE
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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  );
  • 초록

    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.


  • 주제어

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

  • 참고문헌 (19)

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