Relaxation of Free-discontinuity Energies with Obstacles
نویسندگان
چکیده
Given a Borel function ψ defined on a bounded open set Ω with Lipschitz boundary and φ ∈ L1(∂Ω,Hn−1), we prove an explicit representation formula for the L lower semicontinuous envelope of Mumford-Shah type functionals with the obstacle constraint u ≥ ψ Hn−1 a.e. on Ω and the Dirichlet boundary condition u = φ on ∂Ω. Mathematics Subject Classification. 49J45, 74R10. Received December 12, 2006. Revised May 22, 2007. Published online February 7, 2008.
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