Γ-convergence approach to variational problems in perforated domains with Fourier boundary conditions

Valeria Chiadò Piat; Andrey Piatnitski

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 16, Issue: 1, page 148-175
  • ISSN: 1292-8119

Abstract

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The work focuses on the Γ-convergence problem and the convergence of minimizers for a functional defined in a periodic perforated medium and combining the bulk (volume distributed) energy and the surface energy distributed on the perforation boundary. It is assumed that the mean value of surface energy at each level set of test function is equal to zero. Under natural coercivity and p-growth assumptions on the bulk energy, and the assumption that the surface energy satisfies p-growth upper bound, we show that the studied functional has a nontrivial Γ-limit and the corresponding variational problem admits homogenization.


How to cite

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Chiadò Piat, Valeria, and Piatnitski, Andrey. "Γ-convergence approach to variational problems in perforated domains with Fourier boundary conditions." ESAIM: Control, Optimisation and Calculus of Variations 16.1 (2010): 148-175. <http://eudml.org/doc/250721>.

@article{ChiadòPiat2010,
abstract = { The work focuses on the Γ-convergence problem and the convergence of minimizers for a functional defined in a periodic perforated medium and combining the bulk (volume distributed) energy and the surface energy distributed on the perforation boundary. It is assumed that the mean value of surface energy at each level set of test function is equal to zero. Under natural coercivity and p-growth assumptions on the bulk energy, and the assumption that the surface energy satisfies p-growth upper bound, we show that the studied functional has a nontrivial Γ-limit and the corresponding variational problem admits homogenization.
},
author = {Chiadò Piat, Valeria, Piatnitski, Andrey},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Homogenization; Γ-convergence; perforated medium; periodic homogenization; surface term; bulk term},
language = {eng},
month = {1},
number = {1},
pages = {148-175},
publisher = {EDP Sciences},
title = {Γ-convergence approach to variational problems in perforated domains with Fourier boundary conditions},
url = {http://eudml.org/doc/250721},
volume = {16},
year = {2010},
}

TY - JOUR
AU - Chiadò Piat, Valeria
AU - Piatnitski, Andrey
TI - Γ-convergence approach to variational problems in perforated domains with Fourier boundary conditions
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/1//
PB - EDP Sciences
VL - 16
IS - 1
SP - 148
EP - 175
AB - The work focuses on the Γ-convergence problem and the convergence of minimizers for a functional defined in a periodic perforated medium and combining the bulk (volume distributed) energy and the surface energy distributed on the perforation boundary. It is assumed that the mean value of surface energy at each level set of test function is equal to zero. Under natural coercivity and p-growth assumptions on the bulk energy, and the assumption that the surface energy satisfies p-growth upper bound, we show that the studied functional has a nontrivial Γ-limit and the corresponding variational problem admits homogenization.

LA - eng
KW - Homogenization; Γ-convergence; perforated medium; periodic homogenization; surface term; bulk term
UR - http://eudml.org/doc/250721
ER -

References

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