Approximation of planar Sobolev $W^{2,1}$ homeomorphisms by Piecewise Quadratic Homeomorphisms and Diffeomorphisms
Functional Analysis
2020-08-14 v1
Abstract
Given a Sobolev homeomorphism in the plane we find a piecewise quadratic homeomorphism that approximates it up to a set of measure. We show that this piecewise quadratic map can be approximated by diffeomorphisms in the norm on this set.
Cite
@article{arxiv.2008.05736,
title = {Approximation of planar Sobolev $W^{2,1}$ homeomorphisms by Piecewise Quadratic Homeomorphisms and Diffeomorphisms},
author = {Daniel Campbell and Stanislav Hencl},
journal= {arXiv preprint arXiv:2008.05736},
year = {2020}
}