English

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 fW2,1f\in W^{2,1} in the plane we find a piecewise quadratic homeomorphism that approximates it up to a set of ϵ\epsilon measure. We show that this piecewise quadratic map can be approximated by diffeomorphisms in the W2,1W^{2,1} norm on this set.

Keywords

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}
}