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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2603.18819 |
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Sommario:
- Consider a piecewise affine Lipschitz map $ϕ: Ω\to \mathbb R$, where $Ω\subset \mathbb R^d$ is an open set, and assume that $x \mapsto x + t \nabla ϕ(x)$ is injective for almost every $t > 0$. In (J.-G. Liu, R.~L. Pego, \emph{Rigidly breaking potential flows and a countable Alexandrov theorem for polytopes}, Pure Appl. Anal., \textbf{7}(4), 2025) the authors conjecture that every such $ϕ$ must be locally convex. We prove the result assuming additionally $\nabla ϕ\in BV_{loc}(Ω)$, for a more general class of measure preserving maps.