Gamma-limits and relaxations for rate-independent evolutionary problems

This work uses the energetic formulation of rate-independent systems that is based on the stored-energy functionals E and the dissipation distance D. For sequences (Ek )k?N and (Dk )k?N we address the question under which conditions the limits q? of solutions qk : [0, T] -> Qsatisfy a suitable limit problem with limit functionals E? andD?, which are the corresponding -limits. We derive a sufficient condition, called conditional upper semi-continuity of the stable sets, which is essential to guarantee that q? solves the limit problem. In particular, this condition holds if certain joint recovery sequences exist. Moreover, we showthat time-incrementalminimization problems can be used to approximate