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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.
Christopher J. Larsen (2000)
ESAIM: Control, Optimisation and Calculus of Variations
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Benedetti, Irene, Mascolo, Elvira (2004)
Abstract and Applied Analysis
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Mariano Giaquinta, Giuseppe Modica, Jiří Souček (1979)
Commentationes Mathematicae Universitatis Carolinae
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Aikawa, Hiroaki, Ohtsuka, Makoto (1999)
Annales Academiae Scientiarum Fennicae. Mathematica
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Martin Kružík, Agnieszka Kałamajska (2008)
ESAIM: Control, Optimisation and Calculus of Variations
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We use DiPerna’s and Majda’s generalization of Young measures to describe oscillations and concentrations in sequences of gradients, , bounded in if and is a bounded domain with the extension property in . Our main result is a characterization of those DiPerna-Majda measures which are generated by gradients of Sobolev maps satisfying the same fixed Dirichlet boundary condition. Cases where no boundary conditions nor regularity of are required and links with lower semicontinuity...