On a functional depending on curvature and edges
Carlo-Romano Grisanti (2001)
Rendiconti del Seminario Matematico della Università di Padova
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Carlo-Romano Grisanti (2001)
Rendiconti del Seminario Matematico della Università di Padova
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Antonin Chambolle, Gianni Dal Maso (1999)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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Blaise Bourdin (1999)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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Simon Masnou, Jean-Michel Morel (2006)
Rendiconti del Seminario Matematico della Università di Padova
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Andrea Braides, Antonin Chambolle, Margherita Solci (2007)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider, in an open subset of , energies depending on the perimeter of a subset (or some equivalent surface integral) and on a function which is defined only on . We compute the lower semicontinuous envelope of such energies. This relaxation has to take into account the fact that in the limit, the “holes” may collapse into a discontinuity of , whose surface will be counted twice in the relaxed energy. We discuss some situations where such energies appear, and give, as an...