# Relaxation of free-discontinuity energies with obstacles

Matteo Focardi; Maria Stella Gelli

ESAIM: Control, Optimisation and Calculus of Variations (2008)

- Volume: 14, Issue: 4, page 879-896
- ISSN: 1292-8119

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topFocardi, Matteo, and Gelli, Maria Stella. "Relaxation of free-discontinuity energies with obstacles." ESAIM: Control, Optimisation and Calculus of Variations 14.4 (2008): 879-896. <http://eudml.org/doc/250308>.

@article{Focardi2008,

abstract = {
Given a Borel function ψ defined on a bounded open set Ω
with Lipschitz boundary and $\varphi\in L^1(\partial\Omega,\{\mathcal H\}^\{n-1\})$,
we prove an explicit representation formula for the L1 lower
semicontinuous envelope of Mumford-Shah type functionals
with the obstacle constraint $u^+\ge\psi$$\{\mathcal H\}^\{n-1\}$ a.e. on Ω and
the Dirichlet boundary condition $u=\varphi$ on $\partial\Omega$.
},

author = {Focardi, Matteo, Gelli, Maria Stella},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Obstacle problems; Mumford-Shah energy; relaxation; obstacle problems},

language = {eng},

month = {2},

number = {4},

pages = {879-896},

publisher = {EDP Sciences},

title = {Relaxation of free-discontinuity energies with obstacles},

url = {http://eudml.org/doc/250308},

volume = {14},

year = {2008},

}

TY - JOUR

AU - Focardi, Matteo

AU - Gelli, Maria Stella

TI - Relaxation of free-discontinuity energies with obstacles

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2008/2//

PB - EDP Sciences

VL - 14

IS - 4

SP - 879

EP - 896

AB -
Given a Borel function ψ defined on a bounded open set Ω
with Lipschitz boundary and $\varphi\in L^1(\partial\Omega,{\mathcal H}^{n-1})$,
we prove an explicit representation formula for the L1 lower
semicontinuous envelope of Mumford-Shah type functionals
with the obstacle constraint $u^+\ge\psi$${\mathcal H}^{n-1}$ a.e. on Ω and
the Dirichlet boundary condition $u=\varphi$ on $\partial\Omega$.

LA - eng

KW - Obstacle problems; Mumford-Shah energy; relaxation; obstacle problems

UR - http://eudml.org/doc/250308

ER -

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