|Abstract||We show that minimizers of free discontinuity problems with energy dependent on jump integrals and Dirichlet boundary conditions are smooth provided a smallness condition is imposed on data.
We examine several examples, including elastic-plastic beam and plate with free yield lines and deformable body with free damage. In all cases there is a gap between the condition for solvability (safe load condition) and this smallness condition (load regularity condition).
Such gap allows the existence of damaged/creased minimizers. Eventually we provide explicit examples of irregular solutions when the load stays in the gap.|