# A PLANAR SOBOLEV EXTENSION THEOREM FOR PIECEWISE LINEAR HOMEOMORPHISMS

created by radici on 20 Jul 2015
modified on 26 Jan 2016

[BibTeX]

Accepted Paper

Inserted: 20 jul 2015
Last Updated: 26 jan 2016

Journal: Pacific Journal of Mathematics
Year: 2015

Abstract:

We prove that a planar piecewise linear homeomorphism $\varphi$ defined on the boundary of the square can be extended to a homeomorphism $h$ of the whole square, in such a way that $\ h\ _{\mathit{W}^{1,p}}$ is bounded from above by $\ \varphi \ _{\mathit{W}^{1,p}}$ for every $p \geq 1$.