206 citations · 394 across the 45 of their papers we have counts for
60 papers
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 -…
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^…
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…
Measure and dimension theory of permeable sets and its applications to fractals
Gunther Leobacher, Tapio Rajala, Alexander Steinicke +1
We study {\it permeable} sets. These are sets \(Θ\subset \mathbb{R}^d\) which have the property that each two points \(x,y\in \mathbb{R}^d\) can be connected by a short path \(γ\)…
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…
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…
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.…
A necessary condition for Sobolev extension domains in higher dimensions
Miguel García-Bravo, Tapio Rajala, Jyrki Takanen
We give a necessary condition for a domain to have a bounded extension operator from to for the range . The condition is given in ter…
Tensorization of -weak differentiable structures
Sylvester Eriksson-Bique, Tapio Rajala, Elefterios Soultanis
We consider -weak differentiable structures that were recently introduced by the first and last named authors, and prove that the product of -weak charts is a -weak chart.…
Zero volume boundary for extension domains from Sobolev to
Tapio Rajala, Zheng Zhu
In this note, we prove that the boundary of a -extension domain is of volume zero under the assumption that the domain $\boz$ is -fat at almost every $x\in\parti…
Non-Hilbertian tangents to Hilbertian spaces
Danka Lučić, Enrico Pasqualetto, Tapio Rajala
We provide examples of infinitesimally Hilbertian, rectifiable, Ahlfors regular metric measure spaces having pmGH-tangents that are not infinitesimally Hilbertian.
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…
Two-sided boundary points of Sobolev-extension domains on Euclidean spaces
Miguel García-Bravo, Tapio Rajala, Jyrki Takanen
We prove an estimate on the Hausdorff-dimension of the set of two-sided boundary points of general Sobolev-extension domains on Euclidean spaces. We also present examples showing l…
Uniform approximation of continuous couplings
Ugo Bindini, Tapio Rajala
We study the approximation of non-negative multi-variate couplings in the uniform norm while matching given single-variable marginal constraints.
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…
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 -…
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…
Dimension estimates for the boundary of planar Sobolev extension domains
Danka Lučić, Tapio Rajala, Jyrki Takanen
We prove an asymptotically sharp dimension upper-bound for the boundary of bounded simply-connected planar Sobolev -extension domains via the weak mean porosity of the bou…
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.
Indecomposable sets of finite perimeter in doubling metric measure spaces
Paolo Bonicatto, Enrico Pasqualetto, Tapio Rajala
We study a measure-theoretic notion of connectedness for sets of finite perimeter in the setting of doubling metric measure spaces supporting a weak -Poincaré inequality. Th…
Multi-marginal Entropy-Transport with repulsive cost
Augusto Gerolin, Anna Kausamo, Tapio Rajala
In this paper we study theoretical properties of the entropy-transport functional with repulsive cost functions. We provide sufficient conditions for the existence of a minimizer i…
Sharp estimate on the inner distance in planar domains
Danka Lučić, Enrico Pasqualetto, Tapio Rajala
We show that the inner distance inside a bounded planar domain is at most the one-dimensional Hausdorff measure of the boundary of the domain. We prove this sharp result by establi…
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…