Pekka Koskela

activity

20242026

collaborators

4 papers

math.FA2026

Planar $W^{1, 1}$ -extension domains

Pekka Koskela, Tapio Rajala, Yi Ru-Ya Zhang

We show that a bounded planar simply connected domain $I^c ◯$ is a $W^{1, 1}$ -extension domain if and only if for every pair $x, y$ of points in $I^c ◯^{c}$ there exists a curve $Î³\subset…

math.FA2025

Sobolev Versus Homogeneous Sobolev II

Pekka Koskela, Riddhi Mishra, Zheng Zhu

We study the relationship between Sobolev extension domains and homogeneous Sobolev extension domains. Precisely, for a certain range of exponents $p$ and $q$ , we construct a $(W^{…

math.FA2024

Sobolev Versus Homogeneous Sobolev Extension

Pekka Koskela, Riddhi Mishra, Zheng Zhu

In this paper, we study the relationship between Sobolev extension domains and homogeneous Sobolev extension domains. Precisely, we obtain the following results. 1- Let $1\leq q\le…

math.FA2024

The volume of the boundary of a Sobolev $(p, q)$ -extension domain II

Pekka Koskela, Riddhi Mishra

We show that the volume of the boundary of a bounded Sobolev $(p, q)$ -extension domain is zero when $1 \leq q < p < \frac{q n}{( n - q )} .$

Planar W1,1-extension domains

Sobolev Versus Homogeneous Sobolev II

Sobolev Versus Homogeneous Sobolev Extension

The volume of the boundary of a Sobolev (p,q)-extension domain II

Planar $W^{1, 1}$ -extension domains

The volume of the boundary of a Sobolev $(p, q)$ -extension domain II