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

Abstract

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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.

How to cite

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Croce, 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

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  1. H. Attouch, Variational Convergence for Functions and Operators, Applicable Mathematics Series. Pitman Advanced Publishing Program (1985).  
  2. H. Federer, Geometric Measure Theory, Classic in Mathematics. Springer-Verlag (1969).  
  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.  
  4. D. Kinderlehrer and P. Pedregal, Characterization of Young measures generated by gradients. Arch. Rational Mech. Anal.119 (1991) 329–365.  
  5. C. Licht and G. Michaille, A modelling of elastic adhesive bonded joints. Adv. Math. Sci. Appl.7 (1997) 711–740.  
  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.  

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