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

Gisella Croce; Catherine Lacour; Gérard Michaille

ESAIM: Control, Optimisation and Calculus of Variations (2008)

- Volume: 15, Issue: 4, page 818-838
- ISSN: 1292-8119

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topCroce, Gisella, Lacour, Catherine, and 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 15.4 (2008): 818-838. <http://eudml.org/doc/90939>.

@article{Croce2008,

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.
},

author = {Croce, Gisella, Lacour, Catherine, Michaille, Gérard},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Gradient Young measures; concentration measures; minimization problems; quasiconvexity; gradient Young measures},

language = {eng},

month = {7},

number = {4},

pages = {818-838},

publisher = {EDP Sciences},

title = {A characterization of gradient Young-concentration measures generated by solutions of Dirichlet-type problems with large sources},

url = {http://eudml.org/doc/90939},

volume = {15},

year = {2008},

}

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

DA - 2008/7//

PB - EDP Sciences

VL - 15

IS - 4

SP - 818

EP - 838

AB - 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.

LA - eng

KW - Gradient Young measures; concentration measures; minimization problems; quasiconvexity; gradient Young measures

UR - http://eudml.org/doc/90939

ER -

## References

top- H. Attouch, Variational Convergence for Functions and Operators, Applicable Mathematics Series. Pitman Advanced Publishing Program (1985).
- H. Federer, Geometric Measure Theory, Classic in Mathematics. Springer-Verlag (1969). Zbl0176.00801
- I. Fonseca, S. Müller and P. Pedregal, Analysis of concentration and oscillation effects generated by gradients. SIAM J. Math. Anal.29 (1998) 736–756. Zbl0920.49009
- D. Kinderlehrer and P. Pedregal, Characterization of Young measures generated by gradients. Arch. Rational Mech. Anal.119 (1991) 329–365. Zbl0754.49020
- C. Licht and G. Michaille, A modelling of elastic adhesive bonded joints. Adv. Math. Sci. Appl.7 (1997) 711–740. Zbl0892.73007
- 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. Zbl1118.49009

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