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Harnack inequality for a nonlinear parabolic equation under geometric flow
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In this paper, we obtain some gradient estimates for positive solutions to the following nonlinear parabolic equation [수식] under general geometric flow on complete noncompact manifolds, where 0 < σ < 1 is a real constant and b(x, t) is a function which is C2 in the x-variable and C1 in the t-variable. As an application, we get an interesting Harnack inequality.
Abstract
In this paper, we obtain some gradient estimates for positive solutions to the following nonlinear parabolic equation [수식] under general geometric flow on complete noncompact manifolds, where 0 < σ < 1 is a real constant and b(x, t) is a function which is C2 in the x-variable and C1 in the t-variable. As an application, we get an interesting Harnack inequality.
참고문헌 (10)
- T. Aubin, "Nonlinear Analysis on Manifolds. Monge-Amp´re equations" (1982), Springer
- E. Calabi, "An extension of E. Hopf ’s maximum principle with an application to Riemannian geometry", Duke Math. J, 25(1), pp.45~56 (1958)
- R. Hamilton, "A matrix Harnack estimate for the heat equation", Comm. Anal. Geom, 1(1), pp.113~126 (1993)
- S. Kuang, "A gradient estimate for all positive solutions of the conjugate heat equation under Ricci flow", J. Funct. Anal, 255(4), pp.1008~1023 (2008)
- P. Li, "On the parabolic kernel of the Schrodinger operator", Acta Math, 156(3), pp.153~201 (1986)
- S. P. Liu, "Gradient estimates for solutions of the heat equation under Ricci flow", Pacific J. Math, 243(1), pp.165~180 (2009)
- G. Perelman, "The entropy formula for the Ricci flow and its geometric applications", arXiv math.DG, 2002
- J. Sun, "Gradient estimates for positive solutions of the heat equation under geometric flow", Pacific J. Math, 253(2), pp.489~510 (2011)
- J. Zhang, "Gradient estimates for a nonlinear equation △fu + cu−α = 0 on complete noncompact manifolds", Commun. Math, 19(1), pp.73~84 (2011)
- X. B. Zhu, "Gradient estimates and Liouville theorems for nonlinear parabolic equations on noncompact Riemannian manifolds", Nonlinear Anal, 74(15), pp.5141~5146 (2011)
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