Classification of strict limits of planar BV homeomorphisms

We present a classification of m-strict limits (i.e. and |D1fk|(Ω)+|D2fk|(Ω)→|D1f|(Ω)+|D2f|(Ω)) planar BV homeomorphisms; class previously studied by the authors S. Hencl in [6]. There it was shown that such mappings allow for cavitations fractures singularities but fulfil suitable generalization INV condition. As pointed out J. Ball [3], these features are physically expected limit configurations elastic deformations. In work we develop no-crossing condition introduced De Philippis Pratelli [8] to describe weak Sobolev homeomorphisms call condition, show mapping satisfies this property if only can be approximated m-strictly bounded variations.