Displaying similar documents to “Some remarks about a notion of rearrangement”

Relaxation of elastic energies with free discontinuities and constraint on the strain

Andrea Braides, Anneliese Defranceschi, Enrico Vitali (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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As a model for the energy of a brittle elastic body we consider an integral functional consisting of two parts: a volume one (the usual linearly elastic energy) which is quadratic in the strain, and a surface part, which is concentrated along the fractures (i.e. on the discontinuities of the displacement function) and whose density depends on the jump part of the strain. We study the problem of the lower semicontinuous envelope of such a functional under the assumptions that the surface...

A variational model for urban planning with traffic congestion

Guillaume Carlier, Filippo Santambrogio (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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We propose a variational model to describe the optimal distributions of residents and services in an urban area. The functional to be minimized involves an overall transportation cost taking into account congestion effects and two aditional terms which penalize concentration of residents and dispersion of services. We study regularity properties of the minimizers and treat in details some examples.

A quantitative version of the isoperimetric inequality : the anisotropic case

Luca Esposito, Nicola Fusco, Cristina Trombetti (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We state and prove a stability result for the anisotropic version of the isoperimetric inequality. Namely if E is a set with small anisotropic isoperimetric deficit, then E is “close” to the Wulff shape set.