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arXiv · 1804.03449

Weak regularity of the inverse under minimal assumptions

Stanislav Hencl·Aapo Kauranen·Rami Luisto
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Abstract

Let $\Omega\subset\mathbb{R}^3$ be a domain and let $f\in BV_{\operatorname{loc}}(\Omega,\mathbb{R}^3)$ be a homeomorphism such that its distributional adjugate is a finite Radon measure. We show that its inverse has bounded variation $f^{-1}\in BV_{\operatorname{loc}}$. The condition that the distributional adjugate is finite measure is not only sufficient but also necessary for the weak regularity of the inverse.

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Stanislav Hencl, Aapo Kauranen, Rami Luisto. 2018-04-10. Weak regularity of the inverse under minimal assumptions. https://arxiv.org/abs/1804.03449

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