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Relaxation of free-discontinuity energies with obstacles

Matteo Focardi; Maria Stella Gelli — 2008

ESAIM: Control, Optimisation and Calculus of Variations

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

Finite-difference approximation of energies in fracture mechanics

Roberto Alicandro; Matteo Focardi; Maria Stella Gelli — 2000

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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