Global calibrations for the non-homogeneous Mumford-Shah functional

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dc.creatorMorini, Massimiliano
dc.date2001-05-16
dc.date.accessioned2026-07-07T04:41:45Z
dc.date.available2026-07-07T04:41:45Z
dc.descriptionUsing a calibration method we prove that, if $Γ\subset Ω$ is a closed regular hypersurface and if the function $g$ is discontinuous along $Γ$ and regular outside, then the function $u_β$ which solves $$ \begin{cases} Δu_β=β(u_β-g)& \text{in $Ω\setminusΓ$} \partial_ν u_β=0 & \text{on $\partialΩ\cupΓ$} \end{cases} $$ is in turn discontinuous along $Γ$ and it is the unique absolute minimizer of the non-homogeneous Mumford-Shah functional $$ \int_{Ω\setminus S_u}|\nabla u|^2 dx +{\cal H}^{n-1}(S_u)+β\int_{Ω\setminus S_u}(u-g)^2 dx, $$ over $SBV(Ω)$, for $β$ large enough. Applications of the result to the study of the gradient flow by the method of minimizing movements are shown.
dc.description33 pages
dc.identifierhttps://arxiv.org/abs/math/0105141
dc.identifierhttp://arxiv.org/abs/math/0105141
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61485
dc.subjectFunctional Analysis
dc.subject49K10, 49Q20
dc.titleGlobal calibrations for the non-homogeneous Mumford-Shah functional
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