Quasi-static evolution in brittle fracture: the case of bounded   solutions
  The main steps of the proof of the existence result for the quasi-static evolution of cracks in brittle materials, obtained in [7] in the vector case and for a general quasiconvex elastic energy, are presented here under the simplifying assumption that the minimizing sequences involved in the problem are uniformly bounded in $L^\infty$. 
Gianni Dal Maso, Gilles A. Francfort, Rodica Toader