Calculus of Variations and Geometric Measure Theory

D. Campbell - A. Kauranen - E. Radici

Classification of strict limits of planar BV homeomorphisms

created by radici on 22 Jan 2021
modified on 28 Oct 2022



Inserted: 22 jan 2021
Last Updated: 28 oct 2022

Year: 2021

ArXiv: 2101.09013 PDF


We present a classification of strict limits of planar BV homeomorphisms. The authors and S. Hencl showed in a previous work \cite{CHKR} that such mappings allow for cavitations and fractures singularities but fulfill a suitable generalization of the INV condition. As pointed out by J. Ball \cite{B}, these features are physically expected by limit configurations of elastic deformations. In the present work we develop a suitable generalization of the \emph{no-crossing} condition introduced by De Philippis and Pratelli in \cite{PP} to describe weak limits of planar Sobolev homeomorphisms that we call \emph{BV no-crossing} condition, and we show that a planar mapping satisfies this property if and only if it can be approximated strictly by homeomorphisms of bounded variations.