| Issue |
ESAIM: COCV
Volume 14, Number 4, October-December 2008
|
|
|---|---|---|
| Page(s) | 879 - 896 | |
| DOI | https://doi.org/10.1051/cocv:2008014 | |
| Published online | 07 February 2008 | |
Relaxation of free-discontinuity energies with obstacles
1
Dip. Mat. “U. Dini”, V.le Morgagni, 67/a, 50134 Firenze, Italy; focardi@math.unifi.it
2
Dip. Mat. “L. Tonelli”, L.go Bruno Pontecorvo, 5, 56127 Pisa, Italy; gelli@dm.unipi.it
Received:
12
December
2006
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
© EDP Sciences, SMAI, 2008
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