44 citations · 76 across the 14 of their papers we have counts for
11 papers · 1 filter
Extension properties of planar subsets supporting a weak -Poincaré inequality
Miguel García-Bravo, Tapio Rajala
We study Sobolev and -extension properties of planar subsets. In particular, we prove that fat Sierpiński carpets that support a weak -Poincaré inequality are -…
Closed BV-extension and -extension sets
Emanuele Caputo, Jesse Koivu, Danka Lučić +1
This paper studies the relations between extendability of different classes of Sobolev and functions from closed sets in general metric measure spaces. Under the ass…
A note on Laplacian bounds, deformation properties and isoperimetric sets in metric measure spaces
Enrico Pasqualetto, Tapio Rajala
In the setting of length PI spaces satisfying a suitable deformation property, it is known that each isoperimetric set has an open representative. In this paper, we construct an ex…
Approximation by BV-extension sets via perimeter minimization in metric spaces
Jesse Koivu, Danka Lučić, Tapio Rajala
We show that every bounded domain in a metric measure space can be approximated in measure from inside by closed -extension sets. The extension sets are obtained by minimizing…
Strong -extension and -extension domains
Miguel García-Bravo, Tapio Rajala
We show that a bounded domain in a Euclidean space is a -extension domain if and only if it is a strong -extension domain. In the planar case, bounded and strong -…
Approximation by uniform domains in doubling quasiconvex metric spaces
Tapio Rajala
We show that any bounded domain in a doubling quasiconvex metric space can be approximated from inside and outside by uniform domains.