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arXiv · 2312.13078

Constructing diffeomorphisms and homeomorphisms with prescribed derivative

Paweł Goldstein·Zofia Grochulska·Piotr Hajłasz
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Abstract

We prove that for any measurable mapping $T$ into the space of matrices with positive determinant, there is a diffeomorphism whose derivative equals $T$ outside a set of measure less than $\varepsilon$. We use this fact to prove that for any measurable mapping $T$ into the space of matrices with non-zero determinant (with no sign restriction), there is an almost everywhere approximately differentiable homeomorphism whose derivative equals $T$ almost everywhere.

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Paweł Goldstein, Zofia Grochulska, Piotr Hajłasz. 2023-12-20. Constructing diffeomorphisms and homeomorphisms with prescribed derivative. https://arxiv.org/abs/2312.13078

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