A planar Sobolev extension theorem for piecewise linear homeomorphisms

Emanuela Radici

Vol. 283 (2016), No. 2, 405–418

DOI: 10.2140/pjm.2016.283.405

Abstract

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

Keywords

piecewise affine approximation, Sobolev homeomorphisms

Mathematical Subject Classification 2010

Primary: 46E35

Milestones

Received: 26 August 2015

Revised: 25 November 2015

Accepted: 25 January 2016

Published: 22 June 2016