Calculus of Variations and Geometric Measure Theory

D. Percivale - F. Tomarelli

Regular minimizers of some free discontinuity problems

created by tomarelli on 11 Oct 2009
modified on 16 Oct 2009



Inserted: 11 oct 2009
Last Updated: 16 oct 2009

Pages: 1-47
Year: 2009


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 damagedcreased minimizers. Eventually we provide explicit examples of irregular solutions when the load stays in the gap.

Keywords: free discontinuity, bounded hessian, safe load, plastic hinges