Relaxation of free-discontinuity energies with obstacles
Dip. Mat. “U. Dini”, V.le Morgagni, 67/a, 50134 Firenze, Italy; email@example.com
2 Dip. Mat. “L. Tonelli”, L.go Bruno Pontecorvo, 5, 56127 Pisa, Italy; firstname.lastname@example.org
Revised: 22 May 2007
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 .
Mathematics Subject Classification: 49J45 / 74R10
Key words: Obstacle problems / Mumford-Shah energy / relaxation
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