Volume 15, Number 4, October-December 2009
|Page(s)||818 - 838|
|Published online||19 July 2008|
A characterization of gradient Young-concentration measures generated by solutions of Dirichlet-type problems with large sources
LMAH (Laboratoire de Mathématiques Appliquées du Havre), Université du Havre, 25 rue Philippe Lebon, BP 540, 76058 Le Havre, France.
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. firstname.lastname@example.org
3 EMIAN, Université de Nîmes, France. email@example.com
We show how to capture the gradient concentration of the solutions of Dirichlet-type problems subjected to large sources of order 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.
Mathematics Subject Classification: 49Q20 / 28A33
Key words: Gradient Young measures / concentration measures / minimization problems / quasiconvexity
© EDP Sciences, SMAI, 2008
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