Zobrazeno 1 - 10
of 220
pro vyhledávání: '"RAJALA, TAPIO"'
We study {\it permeable} sets. These are sets \(\Theta \subset \mathbb{R}^d\) which have the property that each two points \(x,y\in \mathbb{R}^d\) can be connected by a short path \(\gamma\) which has small (or even empty, apart from the end points o
Externí odkaz:
http://arxiv.org/abs/2410.17254
Autor:
Pasqualetto, Enrico, Rajala, Tapio
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 and to the related tangent bundles.
Comment: 20 pages
Comment: 20 pages
Externí odkaz:
http://arxiv.org/abs/2306.03684
We show that every bounded domain in a metric measure space can be approximated in measure from inside by closed $BV$-extension sets. The extension sets are obtained by minimizing the sum of the perimeter and the measure of the difference between the
Externí odkaz:
http://arxiv.org/abs/2305.02891
We study extensions of sets and functions in general metric measure spaces. We show that an open set has the strong BV extension property if and only if it has the strong extension property for sets of finite perimeter. We also prove several implicat
Externí odkaz:
http://arxiv.org/abs/2302.10018
The tensorization problem for Sobolev spaces asks for a characterization of how the Sobolev space on a product metric measure space $X\times Y$ can be determined from its factors. We show that two natural descriptions of the Sobolev space from the li
Externí odkaz:
http://arxiv.org/abs/2209.03040
We give a necessary condition for a domain to have a bounded extension operator from $L^{1,p}(\Omega)$ to $L^{1,p}(\mathbb R^n)$ for the range $1 < p < 2$. The condition is given in terms of a power of the distance to the boundary of $\Omega$ integra
Externí odkaz:
http://arxiv.org/abs/2207.00541
We consider $p$-weak differentiable structures that were recently introduced by the first and last named authors, and prove that the product of $p$-weak charts is a $p$-weak chart. This implies that the product of two spaces with a $p$-weak different
Externí odkaz:
http://arxiv.org/abs/2206.05046
Autor:
Rajala, Tapio, Zhu, Zheng
In this note, we prove that the boundary of a $(W^{1, p}, BV)$-extension domain is of volume zero under the assumption that the domain $\boz$ is $1$-fat at almost every $x\in\partial\boz$. Especially, the boundary of any planar $(W^{1, p}, BV)$-exten
Externí odkaz:
http://arxiv.org/abs/2205.10801
We provide examples of infinitesimally Hilbertian, rectifiable, Ahlfors regular metric measure spaces having pmGH-tangents that are not infinitesimally Hilbertian.
Comment: 19 pages
Comment: 19 pages
Externí odkaz:
http://arxiv.org/abs/2111.06777
Autor:
Rajala, Tapio, Bindini, Ugo
We study conditions on closed sets $C,F \subset \mathbb{R}$ making the product $C \times F$ removable or non-removable for $W^{1,p}$. The main results show that the Hausdorff-dimension of the smaller dimensional component $C$ determines a critical ex
Externí odkaz:
http://arxiv.org/abs/2111.03381