Poincaré inequality: From remote balls to all balls - Santi Tasena (2018)
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. © 2014 Elsevier Ltd. All rights reserved.