Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
839877 | Nonlinear Analysis: Theory, Methods & Applications | 2014 | 12 Pages |
Abstract
•The uniform Poincare inequality for all balls is obtained using that of the Z-remote balls.•The subset Z can separate the space into two or more connected components.•The result can be applied to prove the Poincare inequality on weighted Dirichlet spaces — a simple example is also given.
It is shown that the Poincaré inequality holds uniformly for all balls whenever it holds for Z-remote balls providing the set Z satisfies some additional conditions including the condition that Z does not separate the space. The aim of this paper is to prove similar results without using this assumption.
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Authors
Santi Tasena, Laurent Saloff-Coste, Sompong Dhompongsa,