Calculus of Variations and Geometric Measure Theory

E. Radici

A planar Sobolev extension theorem for piecewise linear homeomorphisms

created by radici on 20 Jul 2015
modified on 19 Oct 2020


Published Paper

Inserted: 20 jul 2015
Last Updated: 19 oct 2020

Journal: Pacific Journal of Mathematics
Volume: 238
Number: 2
Pages: 405-418
Year: 2016


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 $\
_{\mathit{W}^{1,p}}$ is bounded from above by $\
\varphi \
_{\mathit{W}^{1,p}}$ for every $p \geq 1$.