206 citations · 394 across the 45 of their papers we have counts for
11 papers · 1 filter
Planar -extension domains
Pekka Koskela, Tapio Rajala, Yi Ru-Ya Zhang
We show that a bounded planar simply connected domain is a -extension domain if and only if for every pair of points in there exists a curve $γ\subset Ω^…
Vector calculus on weighted reflexive Banach spaces
Enrico Pasqualetto, Tapio Rajala
We study first-order Sobolev spaces on reflexive Banach spaces via relaxation, test plans, and divergence. We show the equivalence of the different approaches to the Sobolev spaces…
Tensorization of quasi-Hilbertian Sobolev spaces
Sylvester Eriksson-Bique, Tapio Rajala, Elefterios Soultanis
The tensorization problem for Sobolev spaces asks for a characterization of how the Sobolev space on a product metric measure space can be determined from its factors.…
Removability of product sets for Sobolev functions in the plane
Tapio Rajala, Ugo Bindini
We study conditions on closed sets making the product removable or non-removable for . The main results show that the Hausdorff-dimen…
Bi-Lipschitz invariance of planar - and -extension domains
Miguel García-Bravo, Tapio Rajala, Zheng Zhu
We prove that a bi-Lipschitz image of a planar -extension domain is also a -extension domain, and that a bi-Lipschitz image of a planar -extension domain is again…
Characterisation of upper gradients on the weighted Euclidean space and applications
Danka Lučić, Enrico Pasqualetto, Tapio Rajala
In the context of Euclidean spaces equipped with an arbitrary Radon measure, we prove the equivalence among several different notions of Sobolev space present in the literature and…
A density result on Orlicz-Sobolev spaces in the plane
Walter A. Ortiz, Tapio Rajala
We show the density of smooth Sobolev functions in the Orlicz-Sobolev spaces for bounded simply connected planar domains and doub…
Restricting open surjections
Jesus A. Jaramillo, Enrico Le Donne, Tapio Rajala
We show that any continuous open surjection from a complete metric space to another metric space can be restricted to a surjection for which the domain has the same density charact…
A density result for homogeneous Sobolev spaces on planar domains
Debanjan Nandi, Tapio Rajala, Timo Schultz
We show that in a bounded simply connected planar domain the smooth Sobolev functions are dense in the homogeneous Sobolev spaces …
A density problem for Sobolev spaces on Gromov hyperbolic domains
Pekka Koskela, Tapio Rajala, Yi Ru-Ya Zhang
We prove that for a bounded domain which is Gromov hyperbolic with respect to the quasihyperbolic metric, especially when is a finitely connected planar…
Radon-Nikodym property and area formula for Banach homogeneous group targets
Valentino Magnani, Tapio Rajala
We prove a Rademacher-type theorem for Lipschitz mappings from a subset of a Carnot group to a Banach homogeneous group, equipped with a suitably weakened Radon-Nikodym property. W…