Almost uniform domains and Poincaré inequalities
Almost uniform domains and Poincaré inequalities
Here we show existence of numerous subsets of Euclidean and metric spaces that, despite having empty interior, still support Poincar\'e inequalities. Most importantly, our methods do not depend on any rectilinear or self-similar structure of the underlying space. We instead employ the notion of uniform domain of Martio and Sarvas. …