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

RELAXATION OF FREE DISCONTINUITY ENERGIES WITH OBSTACLES / M. Focardi; M.S. Gelli. - In: ESAIM. COCV. - ISSN 1292-8119. - STAMPA. - 14:(2008), pp. 879-896. [10.1051/cocv:2008014]

RELAXATION OF FREE DISCONTINUITY ENERGIES WITH OBSTACLES

FOCARDI, MATTEO;
2008

Abstract

Given a Borel function $\psi$ defined on a bounded open set $\Omega$ with Lipschitz boundary and $\varphi\in L^1(\partial\Omega,H^{n-1})$, we prove an explicit representation formula for the $L^1$ lower semicontinuous envelope of Mumford-Shah type functionals with the obstacle constraint $u^+\ge\psi$ $H^{n-1}$ a.e. on $\Omega$ and the Dirichlet boundary condition $u=\varphi$ on $\partial\Omega$.
2008
14
879
896
M. Focardi; M.S. Gelli
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/344099
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