Regularity of the inverse mapping in Banach function spaces

Anastasia Molchanova, Tomáš Roskovec and Filip Soudský

Mathematische Nachrichten, 2021, vol. 294, issue 12, 2382-2395

Abstract: We study the regularity properties of the inverse of a bilipschitz mapping f belonging to WmXloc$W^m X_{\mathrm{loc}}$, where X is an arbitrary Banach function space. Namely, we prove that the inverse mapping f−1$f^{-1}$ is also in WmXloc$W^m X_{\mathrm{loc}}$. Furthermore, the paper shows that the class of bilipschitz mappings in WmXloc$W^m X_{\mathrm{loc}}$ is closed with respect to composition and multiplication.

Date: 2021
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https://doi.org/10.1002/mana.201900374

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Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:294:y:2021:i:12:p:2382-2395

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