Constructing diffeomorphisms and homeomorphisms with prescribed derivative
Classical Analysis and ODEs
2023-12-21 v1
Abstract
We prove that for any measurable mapping into the space of matrices with positive determinant, there is a diffeomorphism whose derivative equals outside a set of measure less than . We use this fact to prove that for any measurable mapping into the space of matrices with non-zero determinant (with no sign restriction), there is an almost everywhere approximately differentiable homeomorphism whose derivative equals almost everywhere.
Cite
@article{arxiv.2312.13078,
title = {Constructing diffeomorphisms and homeomorphisms with prescribed derivative},
author = {Paweł Goldstein and Zofia Grochulska and Piotr Hajłasz},
journal= {arXiv preprint arXiv:2312.13078},
year = {2023}
}