Calculus of Variations and Geometric Measure Theory
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D. Campbell - A. Kauranen - E. Radici

Classification of Strict limits of planar BV homeomorphisms

created by radici on 22 Jan 2021


Submitted Paper

Inserted: 22 jan 2021
Last Updated: 22 jan 2021

Year: 2021


We present a classification of strict limits of planar BV homeomorphisms. The authors and S. Hencl showed in a previous work 6 that such mappings allow for cavitations and fractures singularities but fulfill 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 BV no-crossing condition, and we show that a planar mapping satisfi es this property if and only if it can be approximated strictly by homeomorphisms of bounded variations


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