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arXiv · 2003.13664

On BV homeomorphisms

Luigi D'Onofrio·Jan Malý·Carlo Sbordone·Roberta Schiattarella
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Abstract

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

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Luigi D'Onofrio, Jan Malý, Carlo Sbordone, Roberta Schiattarella. 2020-03-30. On BV homeomorphisms. https://arxiv.org/abs/2003.13664

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