Equilibrium and absolute minimal states of Mumford-Shah functionals and brittle fracture propagation

By a combination of geometrical and configurational analysis we study the properties of absolute minimal and equilibrium states of general Mumford-Shah functionals, with applications to models of quasistatic brittle fracture propagation. The main results concern the mathematical relations between physical quantities as energy release rate and energy concentration for 3D cracks with complex shapes, seen as outer measures living on the crack edge.