Classification of strict limits of planar BV homeomorphisms
Campbell, D., Kauranen, A., & Radici, E. (2023). Classification of strict limits of planar BV homeomorphisms. Journal of Functional Analysis, 285(3), Article 109953. https://doi.org/10.1016/j.jfa.2023.109953
Julkaistu sarjassa
Journal of Functional AnalysisPäivämäärä
2023Pääsyrajoitukset
Embargo päättyy: 2025-09-01Pyydä artikkeli tutkijalta
Tekijänoikeudet
© 2023 Elsevier
We present a classification of m-strict limits (i.e. fk ∗ f and |D1fk|(Ω)+|D2fk|(Ω) → |D1f |(Ω) + |D2f |(Ω)) 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.
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Elsevier BVISSN Hae Julkaisufoorumista
0022-1236Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/182731480
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The first author was supported by the grant GACR 20-19018Y. The second author was supported by the Academy of Finland (project number 322441).Lisenssi
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