Stability of parabolic Harnack inequalities

被引：69

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.

引用

页码：1501 / 1533

页数：33

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