Classification of strict limits of planar BV homeomorphisms

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F23%3A50020438" target="_blank" >RIV/62690094:18470/23:50020438 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0022123623001106?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022123623001106?via%3Dihub</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jfa.2023.109953" target="_blank" >10.1016/j.jfa.2023.109953</a>

Result language
angličtina
Original language name
Classification of strict limits of planar BV homeomorphisms
Original language description
We present a classification of m-strict limits (i.e. fk (*)-> f and *|D1f(k)|(Omega) + |D(2)f(k)|(Omega) -> |D(1)f |(Omega) + |D(2)f |(Omega)) of planar BV homeomorphisms; a class previously studied by the authors and S. Hencl in [6]. There it was shown that such mappings allow for cavitations and fractures singularities but fulfil a suitable generalization of the INV condition. As pointed out by J. Ball [3], these features are physically expected by limit configurations of elastic deformations. In the present work we develop a suitable generalization of the no-crossing condition introduced by De Philippis and Pratelli in [8] to describe weak limits of planar Sobolev homeomorphisms that we call the no -crossing BV condition, and we show that a planar mapping satisfies this property if and only if it can be approximated m-strictly by homeomorphisms of bounded variations. (c) 2023 Elsevier Inc. All rights reserved.
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
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GJ20-19018Y" target="_blank" >GJ20-19018Y: Delicate analytical and topological tools for variational problems and modelling</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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