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

Published online by Cambridge University Press:  19 July 2008

Gisella Croce ,
Catherine Lacour  and
Gérard Michaille
Gisella Croce
Affiliation:
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
Catherine Lacour
Affiliation:
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
Gérard Michaille
Affiliation:
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 EMIAN, Université de Nîmes, France. micha@math.univ-montp2.fr
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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 ε-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.

Keywords

Gradient Young measuresconcentration measuresminimization problemsquasiconvexity
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 15 , Issue 4 , October 2009 , pp. 818 - 838
Copyright
© EDP Sciences, SMAI, 2008

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References

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