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Issue ESAIM: COCV
Volume 15, Number 4, October-December 2009
Page(s) 818 - 838
DOI 10.1051/cocv:2008048
Published online 19 July 2008

ESAIM: COCV 15 (2009) 818-838
DOI: 10.1051/cocv:2008048

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

Gisella Croce1, Catherine Lacour2 and Gérard Michaille2, 3

1  LMAH (Laboratoire de Mathématiques Appliquées du Havre), Université du Havre, 25 rue Philippe Lebon, BP 540, 76058 Le Havre, France. gisella.croce@univ-lehavre.fr
2  I3M (Institut de Mathématiques et de Modélisation de Montpellier), UMR-CNRS 5149, Université Montpellier II, Case courrier 051, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France. lacour@math.univ-montp2.fr
3  EMIAN, Université de Nîmes, France. micha@math.univ-montp2.fr


Received January 7, 2008. Published online July 19, 2008.

Abstract
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.


Mathematics Subject Classification. 49Q20, 28A33

Key words: Gradient Young measures, concentration measures, minimization problems, quasiconvexity


© EDP Sciences, SMAI 2008


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