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 (2009)

  • 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 (2009): 818-838. <http://eudml.org/doc/245865>.

@article{Croce2009,
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 $\varepsilon $-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},
language = {eng},
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/245865},
volume = {15},
year = {2009},
}

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
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 $\varepsilon $-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
UR - http://eudml.org/doc/245865
ER -

References

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  1. [1] H. Attouch, Variational Convergence for Functions and Operators, Applicable Mathematics Series. Pitman Advanced Publishing Program (1985). Zbl0561.49012MR773850
  2. [2] H. Federer, Geometric Measure Theory, Classic in Mathematics. Springer-Verlag (1969). Zbl0176.00801MR257325
  3. [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. Zbl0920.49009MR1617712
  4. [4] D. Kinderlehrer and P. Pedregal, Characterization of Young measures generated by gradients. Arch. Rational Mech. Anal. 119 (1991) 329–365. Zbl0754.49020MR1120852
  5. [5] C. Licht and G. Michaille, A modelling of elastic adhesive bonded joints. Adv. Math. Sci. Appl. 7 (1997) 711–740. Zbl0892.73007MR1476274
  6. [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. Zbl1118.49009MR2317338

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