English

On BV homeomorphisms

Classical Analysis and ODEs 2021-01-29 v1

Abstract

We obtain the rectifiability of the graph of a bounded variation homeomorphism ff in the plane and relations between gradients of ff and its inverse. Further, we show an example of a bounded variation homeomorphism ff in the plane which satisfies the (N)(N) and (N1)(N^{-1}) properties and strict positivity of Jacobian of both itself and its inverse, but neither ff nor f1f^{-1} is Sobolev.

Keywords

Cite

@article{arxiv.2003.13664,
  title  = {On BV homeomorphisms},
  author = {Luigi D'Onofrio and Jan Malý and Carlo Sbordone and Roberta Schiattarella},
  journal= {arXiv preprint arXiv:2003.13664},
  year   = {2021}
}
R2 v1 2026-06-23T14:32:29.439Z