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.

We show how to capture the gradient concentration of the solutions of Dirichlet-type problems subjected to large sources of order 1 ε 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.

DOI: 10.1051/cocv:2008048
Classification: 49Q20, 28A33
Keywords: gradient Young measures, concentration measures, minimization problems, quasiconvexity
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     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},
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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/

[1] H. Attouch, Variational Convergence for Functions and Operators, Applicable Mathematics Series. Pitman Advanced Publishing Program (1985). | MR | Zbl

[2] H. Federer, Geometric Measure Theory, Classic in Mathematics. Springer-Verlag (1969). | MR | Zbl

[3] I. Fonseca, S. Müller and P. Pedregal, Analysis of concentration and oscillation effects generated by gradients. SIAM J. Math. Anal. 29 (1998) 736-756. | MR | Zbl

[4] D. Kinderlehrer and P. Pedregal, Characterization of Young measures generated by gradients. Arch. Rational Mech. Anal. 119 (1991) 329-365. | MR | Zbl

[5] C. Licht and G. Michaille, A modelling of elastic adhesive bonded joints. Adv. Math. Sci. Appl. 7 (1997) 711-740. | MR | Zbl

[6] C. Licht, G. Michaille and S. Pagano, A model of elastic adhesive bonded joints through oscillation-concentration measures. J. Math. Pures Appl. 87 (2007) 343-365. | MR | Zbl

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