If $\Omega_j\in \RR^d$ are bounded open subsets and $\Phi\in C^1(\Omega_1\,;\,\Omega_2)$ respects Lebesgue measure and satisfies $F\circ \Phi\in BV(\Omega_1)$ for all $F\in BV(\Omega_2)$ then $\Phi$ is uniformly Lipschitzean.
C^1 Measure Respecting Maps Preserve BV Iff they have Bounded Derivative
COLOMBINI, FERRUCCIO;
2011-01-01
Abstract
If $\Omega_j\in \RR^d$ are bounded open subsets and $\Phi\in C^1(\Omega_1\,;\,\Omega_2)$ respects Lebesgue measure and satisfies $F\circ \Phi\in BV(\Omega_1)$ for all $F\in BV(\Omega_2)$ then $\Phi$ is uniformly Lipschitzean.File in questo prodotto:
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