Published Paper
Inserted: 21 dec 2006
Last Updated: 19 dec 2011
Journal: ESAIM COCV
Volume: 14
Number: 4
Pages: 879--896
Year: 2008
Abstract:
Given a Borel function $\psi$ defined on a bounded open set $\Omega$ with Lipschitz boundary and $\varphi\in L^1(\partial\Omega,{\mathcal H}^{n-1})$, we prove an explicit representation formula for the $L^1$ lower semicontinuous envelope of Mumford-Shah type functionals with the obstacle constraint $u^+> \psi$ ${\mathcal H}^{n-1}$ a.e. on $\Omega$ and the Dirichlet boundary condition $u=\varphi$ on $\partial\Omega$.
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