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Based on a previous work by the authors on the modelling of cavitation and fracture in nonlinear elasticity, we give an alternative proof of a recent result by Csörnyei, Hencl and Malý on the regularity of the inverse of homeomorphisms in the Sobolev space   . With this aim, we show that the notion of fracture surface introduced by the authors in their model corresponds precisely to the original notion of cavity surface in the cavitation models of Müller and Spector (1995) and Conti and De Lellis (2003). We also find that the surface energy introduced in the model for cavitation and fracture is related to Lusin's condition (N) on the non-creation of matter.

Lusin's condition and the distributional determinant for deformations with finite energy