Dimension estimates for the boundary of planar Sobolev extension domains
Classical Analysis and ODEs
2020-06-26 v1 Functional Analysis
Abstract
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 boundary. The sharpness of our estimate is shown by examples.
Keywords
Cite
@article{arxiv.2006.14213,
title = {Dimension estimates for the boundary of planar Sobolev extension domains},
author = {Danka Lučić and Tapio Rajala and Jyrki Takanen},
journal= {arXiv preprint arXiv:2006.14213},
year = {2020}
}
Comments
16 pages, 4 figures