Characterisation of Area-Strict Limits of Planar BV Homeomorphisms

Explore a comprehensive analysis of area-strict limits of planar BV homeomorphisms in this 40-minute conference talk from the Workshop on "Between Regularity and Defects: Variational and Geometrical Methods in Materials Science" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the classification of mappings that allow for cavitations and fractures while fulfilling a generalized INV condition, as proposed by J. Ball for limit configurations of elastic deformations. Examine the recent work by De Philippis and Pratelli on the no-crossing condition characterizing the Sobolev W^{1,p} closure of planar homeomorphisms. Discover how a generalized version of this concept is equivalent to a map being the area-strict limit of BV homeomorphisms, based on joint research with Daniel Campbell and Aapo Kauranen.