Balanced Viscosity (BV) solutions to infinite-dimensional rate-independent systems

Balanced Viscosity solutions to rate-independent systems arise as limits of reg-ularized rate-independent flows by adding a superlinear vanishing-viscosity dissipa-tion. We address the main issue of proving the existence of such limits for infinite-dimensional systems and of characterizing them by a couple of variational properties that combine a local stability condition and a balanced energy-dissipation identity. A careful description of the jump behavior of the solutions, of their differen-tiability properties, and of their equivalent representation by time rescaling is also presented. Our techniques rely on a suitable chain-rule inequality for functions of bounded variation in Banach spaces, on refined lower-semicontinuity compactness arguments