Jyrki Takanen

activity

20202022

collaborators

4 papers

math.AP2022

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 $L^{1, p} (Ω)$ to $L^{1, p} (R^{n})$ for the range $1 < p < 2$ . The condition is given in ter…

math.CA2021

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…

math.CA2021

Dimension estimate for the two-sided points of planar Sobolev extension domains

Jyrki Takanen

In this paper we give an estimate for the Hausdorff dimension of the set of two-sided points of the boundary of bounded simply connected Sobolev $W^{1, p}$ -extension domain for $1<p…

math.CA2020

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 $W^{1, p}$ -extension domains via the weak mean porosity of the bou…