Relaxation of free-discontinuity energies with obstacles
Matteo Focardi, Maria Stella Gelli · ESAIM Control Optimisation and Calculus of Variations · 2008
Given a Borel function ψ defined on a bounded open set Ω with Lipschitz boundary and , we prove an explicit representation formula for the L1 lower semicontinuous envelope of Mumford-Shah type functionals with the obstacle constraint a.e. on Ω and the Dirichlet boundary condition on .