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

Gisella Croce (1) , Catherine Lacour (2) , Gérard Michaille (2, 3)

1 LMAH - Laboratoire de Mathématiques Appliquées du Havre
2 ACSIOM - Analyse, Calcul Scientifique Industriel et Optimisation de Montpellier
3 UNIMES - Université de Nîmes

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.

Mots clés: quasiconvexity; Gradient Young measures; concentration measures; minimization problems

Domaines: Analyse numérique [math.NA]

Gisella Croce, Catherine Lacour, Gérard Michaille. A characterization of gradient Young-concentration measures generated by solutions of Dirichlet-type problems with large sources. ESAIM: Control, Optimisation and Calculus of Variations, 2008, pp.2008048. ⟨10.1051/cocv:2008048⟩. ⟨hal-00369367⟩