Relaxation of free-discontinuity energies with obstacles
ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 4, pp. 879-896.

Given a Borel function ψ defined on a bounded open set Ω with Lipschitz boundary and ϕL 1 (Ω, n-1 ), we prove an explicit representation formula for the L 1 lower semicontinuous envelope of Mumford-Shah type functionals with the obstacle constraint u + ψ n-1 a.e. on Ω and the Dirichlet boundary condition u=ϕ on Ω.

DOI : https://doi.org/10.1051/cocv:2008014
Classification : 49J45,  74R10
Mots clés : obstacle problems, Mumford-Shah energy, relaxation
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     title = {Relaxation of free-discontinuity energies with obstacles},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {879--896},
     publisher = {EDP-Sciences},
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Focardi, Matteo; Gelli, Maria Stella. Relaxation of free-discontinuity energies with obstacles. ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 4, pp. 879-896. doi : 10.1051/cocv:2008014. http://www.numdam.org/articles/10.1051/cocv:2008014/

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