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A characterization of gradient Young-concentration measures generated by solutions of Dirichlet-type problems with large sources
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A characterization of gradient Young-concentration measures generated by solutions of Dirichlet-type problems with large sources

Gisella Croce, Catherine Lacour et Gérard Michaille
ESAIM: Control, Optimisation and Calculus of Variations
2008

Résumé

quasiconvexity Gradient Young measures concentration measures minimization problems 49Q20, 28A33
We show how to capture the gradient concentration of the solutions of Dirichlet-type problems subjected to large sources of order ${1\over \sqrt \varepsilon}$ concentrated on an $\varepsilon$-neighborhood of a hypersurface of the domain. To this end we define the gradient Young-concentration measures generated by sequences of finite energy and establish a very simple characterization of these measures.

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