We show how to capture the gradient concentration of the solutions of Dirichlet-type problems subjected to large sources of order $\frac{1}{\sqrt{\epsilon}}$ concentrated on an $\epsilon $-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 measures, concentration measures, minimization problems, quasiconvexity

@article{COCV_2009__15_4_818_0, author = {Croce, Gisella and Lacour, Catherine and Michaille, G\'erard}, title = {A characterization of gradient {Young-concentration} measures generated by solutions of {Dirichlet-type} problems with large sources}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {818--838}, publisher = {EDP-Sciences}, volume = {15}, number = {4}, year = {2009}, doi = {10.1051/cocv:2008048}, mrnumber = {2567247}, zbl = {1175.49039}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv:2008048/} }

TY - JOUR AU - Croce, Gisella AU - Lacour, Catherine AU - Michaille, Gérard TI - A characterization of gradient Young-concentration measures generated by solutions of Dirichlet-type problems with large sources JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2009 SP - 818 EP - 838 VL - 15 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2008048/ DO - 10.1051/cocv:2008048 LA - en ID - COCV_2009__15_4_818_0 ER -

%0 Journal Article %A Croce, Gisella %A Lacour, Catherine %A Michaille, Gérard %T A characterization of gradient Young-concentration measures generated by solutions of Dirichlet-type problems with large sources %J ESAIM: Control, Optimisation and Calculus of Variations %D 2009 %P 818-838 %V 15 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2008048/ %R 10.1051/cocv:2008048 %G en %F COCV_2009__15_4_818_0

Croce, Gisella; Lacour, Catherine; Michaille, Gérard. A characterization of gradient Young-concentration measures generated by solutions of Dirichlet-type problems with large sources. ESAIM: Control, Optimisation and Calculus of Variations, Volume 15 (2009) no. 4, pp. 818-838. doi : 10.1051/cocv:2008048. http://archive.numdam.org/articles/10.1051/cocv:2008048/

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