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 05 Jun 2024


Published Paper

Inserted: 22 jan 2021
Last Updated: 5 jun 2024

Journal: Journal of Functional Analysis
Year: 2023

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.