Classification of area-strict limits of planar BV homeomorphisms

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10512297" target="_blank" >RIV/00216208:11320/25:10512297 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=pQcRgmoBZs" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=pQcRgmoBZs</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1112/jlms.70172" target="_blank" >10.1112/jlms.70172</a>

Result language
angličtina
Original language name
Classification of area-strict limits of planar BV homeomorphisms
Original language description
We present a classification of area-strict limits of planar BV$BV$ homeomorphisms. This class of mappings allows for cavitations and fractures but fulfil a suitable generalisation of the INV condition of M & uuml;ller and Spector (Arch. Rational Mech. Anal. 131 (1995), no. 1, 1-66). As pointed out by J. Ball, these features are expected in limit configurations of elastic deformations. De Philippis and Pratelli introduced the no-crossing condition which characterises the W1,p$W<^>{1,p}$ closure of planar homeomorphisms. In the current paper, we show that a suitable version of this concept is equivalent with a map, f$f$, being the area-strict limit of BV homeomorphisms. This extends our results from Campbell et al. (J. Funct. Anal. 285 (2023), no. 3, Paper No. 109953, 30), where we proved that the no-crossing BV condition for a BV map was equivalent with the map being the m-strict limit of homeomorphisms (i.e. and |D1fk|(Omega)+|D2fk|(Omega)->|D1f|(Omega)+|D2f|(Omega)$|{D}_{1}{f}_{k}|(mathrm{Omega})+|{D}_{2}{f}_{k}|(mathrm{Omega})to |{D}_{1}f|(mathrm{Omega})+|{D}_{2}f|(mathrm{Omega})$). Further, we show that the no-crossing BV condition is equivalent with a seemingly stronger version of the same condition.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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