L-harmonic functions with polynomial growth of a fixed rate

2009 ◽  
Vol 52 (12) ◽  
pp. 2855-2862
Author(s):  
ChaoHui Zhou ◽  
ZhiHua Chen
Keyword(s):  
Harmonic Functions ◽  
Polynomial Growth ◽  
Fixed Rate

scholarly journals Polynomial growth harmonic functions on finitely generated abelian groups

2013 ◽  
Vol 44 (4) ◽  
pp. 417-432 ◽  
Author(s):  
Bobo Hua ◽  
Jürgen Jost ◽  
Xianqing Li-Jost
Keyword(s):  
Harmonic Functions ◽  
Polynomial Growth ◽  
Abelian Groups ◽  
Finitely Generated

scholarly journals Dimensional Bounds for Ancient Caloric Functions on Graphs

2019 ◽  
Author(s):  
Bobo Hua
Keyword(s):  
Harmonic Functions ◽  
Polynomial Growth ◽  
Volume Growth ◽  
Heat Equations ◽  
Ancient Solutions

Abstract We study ancient solutions of polynomial growth to heat equations on graphs and extend Colding and Minicozzi’s theorem [9] on manifolds to graphs: for a graph of polynomial volume growth, the dimension of the space of ancient solutions of polynomial growth is bounded by the product of the growth degree and the dimension of harmonic functions with the same growth.

scholarly journals Polynomial growth harmonic functions on groups of polynomial volume growth

2015 ◽  
Vol 280 (1-2) ◽  
pp. 551-567 ◽  
Author(s):  
Bobo Hua ◽  
Jürgen Jost
Keyword(s):  
Harmonic Functions ◽  
Polynomial Growth ◽  
Volume Growth

Sobolev Inequalities and Harmonic Functions of Polynomial Growth

1993 ◽  
Vol s2-48 (3) ◽  
pp. 452-464 ◽  
Author(s):  
G. Alexopoulos ◽  
N. Lohoué
Keyword(s):  
Harmonic Functions ◽  
Polynomial Growth ◽  
Sobolev Inequalities

scholarly journals Ancient Caloric Functions on Graphs With Unbounded Laplacians

2020 ◽  
Author(s):  
Bobo Hua
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Harmonic Functions ◽  
Polynomial Growth ◽  
Volume Growth ◽  
Heat Equations ◽  
Intrinsic Metric ◽  
Ancient Solutions

Abstract We study ancient solutions of polynomial growth to both continuous-time and discrete-time heat equations on graphs with unbounded Laplacians. We extend Colding and Minicozzi’s theorem [12] on manifolds and the result [22] on graphs with normalized Laplacians to the setting of graphs with unbounded Laplacians: for a graph admitting an intrinsic metric, which has polynomial volume growth, the dimension of the space of ancient solutions of polynomial growth is bounded by the dimension of harmonic functions with the same growth up to some factor.

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