Regularity of weak solutions to rate-independent systems in   one-dimension
  We show that under some appropriate assumptions, every weak solution (e.g. energetic solution) to a given rate-independent system is of class SBV, or has finite jumps, or is even piecewise $C^1$. Our assumption is essentially imposed on the energy functional, but not convexity is required. 
Mach Nguyet Minh
math.AP