Calculus of Variations and Geometric Measure Theory
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E. Radici

A planar Sobolev extension theorem for piecewise linear homeomorphisms

created by radici on 20 Jul 2015
modified on 30 Jan 2018

[BibTeX]

Published Paper

Inserted: 20 jul 2015
Last Updated: 30 jan 2018

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

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 $p \geq 1$.


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