Stability of parabolic Harnack inequalities

被引：67
|
作者：
Barlow, MT [1 ]
Bass, RF
机构：
[1] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada
[2] Univ Connecticut, Dept Math, Storrs, CT 06269 USA
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2004年 / 356卷 / 04期
关键词：
Harnack inequality; random walks on graphs; volume doubling; Green functions; Poincare inequality; Sobolev inequality; anomalous diffusion;
D O I：
10.1090/S0002-9947-03-03414-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let (G,E) be a graph with weights {a(xy)} for which a parabolic Harnack inequality holds with space-time scaling exponent betagreater than or equal to2. Suppose {a'(xy)} is another set of weights that are comparable to {a(xy)}. We prove that this parabolic Harnack inequality also holds for (G,E) with the weights {a'(xy)}. We also give stable necessary and sufficient conditions for this parabolic Harnack inequality to hold.
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页码：1501 / 1533
页数：33
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