Extension properties of planar subsets supporting a weak $(1,1)$-Poincaré inequality

Miguel García-Bravo, Tapio Rajala

We study Sobolev and $BV$-extension properties of planar subsets. In particular, we prove that fat Sierpiński carpets that support a weak $(1,1)$-Poincaré inequality are $W^{1,1}$-…