Acta mathematica scientia,Series B ›› 2018, Vol. 38 ›› Issue (6): 1751-1758.
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Yong LIN1, Hongye SONG1,2
Received:2017-08-10
Revised:2018-01-26
Online:2018-12-25
Published:2018-12-28
Contact:
Hongye SONG
E-mail:songhongye@bisu.edu.cn
Supported by:Yong LIN, Hongye SONG. HARNACK AND MEAN VALUE INEQUALITIES ON GRAPHS[J].Acta mathematica scientia,Series B, 2018, 38(6): 1751-1758.
| [1] Yau S T. Harmonic functions on complete Riemannian manifolds. Comm Pure Appl Math, 1975, 28:201-228 [2] Cheng S Y, Yau S T. Differential equations on Riemannian manifolds and their geometric applications. Comm Pure Appl Math, 1975, 27:333-354 [3] Li P, Yau S T. On the parabolic kernel of the Schrödinger operator. Acta Math, 1986, 156:153-201 [4] Li J. Gradient estimates and Harnack inequalities for nonlinear parabolic and nonlinear elliptic equations on Riemannian manifolds. J Funct Anal, 1991, 100:233-256 [5] Negrin E. Gradient estimates and a Liouville type theorem for the Schrödinger operator. J Funct Anal, 1995, 127:198-203 [6] Ma L. Gradient estimates for a simple elliptic equation on non-compact Riemannian manifolds. J Funct Anal, 2006, 241:374-382 [7] Yang Y. Gradient estimates for a nonlinear parabolic equation on Riemannian manifolds. Proc Amer Math Soc, 2008, 136:4095-4102 [8] Yang Y. Gradient estimates for the equation △u + cu-α=0 on Riemannian manifolds. Acta Math Sinica, English Series, 2010, 26:1177-1182 [9] Bauer F, Horn P, Lin Y, Lippner G, Mangoubi D, Yau S T. Li-Yau inequality on graphs. J Differential Geom, 2015, 99:359-405 [10] Lin Y, Liu S, Yang Y. Global gradient estimate on graph and its applications. Acta Math Sin, Engl Ser, 2016, 32:1350-1356 [11] Lin Y, Liu S, Yang Y. A gradient estimate for positive functions on graphs. J Geom Anal, 2017, 27:1667-1679 [12] Li P, Schoen R. Lp and mean value properties of subharmonic functions on Riemannian manifolds. Acta Math, 1984, 153:279-301 [13] Holopainen I, Soardi P M. A strong Liouville theorem for p-harmonic functions on graphs. Ann Acad Sci Fenn Math, 1997, 22:205-226 [14] Holopainen I, Soardi P M. p-harmonic functions on graphs and manifolds. Manuscripta Math, 1997, 94:95-110 [15] Rigoli M, Salvatori M, Vignati M. Subharmonic functions on graphs. Israel J Math, 1997, 99:1-27 [16] Lin Y, Xi L. Lipschitz property of harmonic function on graphs. J Math Anal Appl, 2010, 366:673-678 [17] Hua B, Jost J. Lq harmonic functions on graphs. Israel J Math, 2014, 202:475-490 [18] Karp L. Subharmonic functions on real and complex manifolds. Math Z, 1982, 179:535-554 [19] Lin Y, Yau S T. Ricci curvature and eigenvalue estimate on locally finite graphs. Math Res Lett, 2010, 17:343-356 [20] Grigor'yan A. Analysis on Graphs, Lecture Notes. University Bielefeld, 2009 |
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