Abstract
We show that there exists a planar Jordan domains $\Omega$ with boundary of Hausdorff dimension $1$ such that, for any conformal maps $\varphi \colon \mathbb D \to \Omega$, any homeomorphic extension of $\varphi$ or $\varphi^{-1}$ to the entire plane is not in $W^{1,\,1}_{\rm loc}$ (or even not in $BV_{\rm loc}$).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Annales Academiae Scientiarum Fennicae Mathematica
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
