# 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

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topChiadò 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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