Γ-convergence of functionals on divergence-free fields

Nadia Ansini; Adriana Garroni

ESAIM: Control, Optimisation and Calculus of Variations (2007)

  • Volume: 13, Issue: 4, page 809-828
  • ISSN: 1292-8119

Abstract

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We study the stability of a sequence of integral functionals on divergence-free matrix valued fields following the direct methods of Γ-convergence. We prove that the Γ-limit is an integral functional on divergence-free matrix valued fields. Moreover, we show that the Γ-limit is also stable under volume constraint and various type of boundary conditions.

How to cite

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Ansini, Nadia, and Garroni, Adriana. "Γ-convergence of functionals on divergence-free fields." ESAIM: Control, Optimisation and Calculus of Variations 13.4 (2007): 809-828. <http://eudml.org/doc/250011>.

@article{Ansini2007,
abstract = { We study the stability of a sequence of integral functionals on divergence-free matrix valued fields following the direct methods of Γ-convergence. We prove that the Γ-limit is an integral functional on divergence-free matrix valued fields. Moreover, we show that the Γ-limit is also stable under volume constraint and various type of boundary conditions. },
author = {Ansini, Nadia, Garroni, Adriana},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {$\{\cal A\}$-quasiconvexity; divergence-free fields; Γ-convergence; homogenization; -convergence; functionals on divergence free matrix-valued functions; -quasiconvexity; volume constraints},
language = {eng},
month = {9},
number = {4},
pages = {809-828},
publisher = {EDP Sciences},
title = {Γ-convergence of functionals on divergence-free fields},
url = {http://eudml.org/doc/250011},
volume = {13},
year = {2007},
}

TY - JOUR
AU - Ansini, Nadia
AU - Garroni, Adriana
TI - Γ-convergence of functionals on divergence-free fields
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2007/9//
PB - EDP Sciences
VL - 13
IS - 4
SP - 809
EP - 828
AB - We study the stability of a sequence of integral functionals on divergence-free matrix valued fields following the direct methods of Γ-convergence. We prove that the Γ-limit is an integral functional on divergence-free matrix valued fields. Moreover, we show that the Γ-limit is also stable under volume constraint and various type of boundary conditions.
LA - eng
KW - ${\cal A}$-quasiconvexity; divergence-free fields; Γ-convergence; homogenization; -convergence; functionals on divergence free matrix-valued functions; -quasiconvexity; volume constraints
UR - http://eudml.org/doc/250011
ER -

References

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