Continuous limits of discrete perimeters

Antonin Chambolle; Alessandro Giacomini; Luca Lussardi

Displaying similar documents to “Continuous limits of discrete perimeters”

Non-local approximation of free-discontinuity problems with linear growth

Luca Lussardi, Enrico Vitali (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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We approximate, in the sense of -convergence, free-discontinuity functionals with linear growth in the gradient by a sequence of non-local integral functionals depending on the average of the gradients on small balls. The result extends to higher dimension what we already proved in the one-dimensional case.

Lower semicontinuity and relaxation results in BV for integral functionals with BV integrands

Nicola Fusco, Virginia De Cicco, Micol Amar (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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New $L^{1}$ -lower semicontinuity and relaxation results for integral functionals defined in BV( $Ω$ ) are proved, under a very weak dependence of the integrand with respect to the spatial variable $x$ . More precisely, only the lower semicontinuity in the sense of the $1$ -capacity is assumed in order to obtain the lower semicontinuity of the functional. This condition is satisfied, for instance, by the lower approximate limit of the integrand, if it is BV with respect to $x$ . Under this further BV dependence,...

A-quasiconvexity : weak-star convergence and the gap

Irene Fonseca, Giovanni Leoni, Stefan Müller (2004)

Annales de l'I.H.P. Analyse non linéaire

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Eigenvalue problems for degenerate nonlinear elliptic equations in anisotropic media.

Motreanu, Dumitru, Rădulescu, Vicenţiu (2005)

Boundary Value Problems [electronic only]

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A vanishing viscosity approach to a quasistatic evolution problem with nonconvex energy

Alice Fiaschi (2009)

Annales de l'I.H.P. Analyse non linéaire

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Relaxation of free-discontinuity energies with obstacles

Matteo Focardi, Maria Stella Gelli (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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