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## A-Quasiconvexity: Relaxation and Homogenization

ESAIM: COCV, 5 (2000) 539-577

## A -quasiconvexity: weak-star convergence and the gap

Irene Fonseca, Giovanni Leoni and Stefan Müller
Annales de l'Institut Henri Poincare (C) Non Linear Analysis 21 (2) 209 (2004)
DOI: 10.1016/j.anihpc.2003.01.003

## Shape optimization of light structures and the vanishing mass conjecture

Jean-François Babadjian, Flaviana Iurlano and Filip Rindler
Duke Mathematical Journal 172 (1) (2023)
DOI: 10.1215/00127094-2022-0031

## Applied Mathematical Analysis: Theory, Methods, and Applications

Hélia Serrano
Studies in Systems, Decision and Control, Applied Mathematical Analysis: Theory, Methods, and Applications 177 233 (2020)
DOI: 10.1007/978-3-319-99918-0_8

## Weak Lower Semicontinuity of Integral Functionals and Applications

Barbora Benešová and Martin Kružík
SIAM Review 59 (4) 703 (2017)
DOI: 10.1137/16M1060947

## Asymptotic Rigidity of Layered Structures and Its Application in Homogenization Theory

Fabian Christowiak and Carolin Kreisbeck
Archive for Rational Mechanics and Analysis 235 (1) 51 (2020)
DOI: 10.1007/s00205-019-01418-0

## Relaxation and Γ-Convergence of the Energy Functionals of a Two-Phase Elastic Medium

A. V. Dem’yanov
Journal of Mathematical Sciences 128 (5) 3177 (2005)
DOI: 10.1007/s10958-005-0263-3

## Generalized Multiscale Young Measures

SIAM Journal on Mathematical Analysis 52 (4) 3252 (2020)
DOI: 10.1137/19M1238848

## Michell trusses in two dimensions as a $$\Gamma$$ Γ -limit of optimal design problems in linear elasticity

Heiner Olbermann
Calculus of Variations and Partial Differential Equations 56 (6) (2017)
DOI: 10.1007/s00526-017-1266-x

## Polyconvexity for functions of a system of closed differential forms

M. Šilhavý
Calculus of Variations and Partial Differential Equations 57 (1) (2018)
DOI: 10.1007/s00526-017-1298-2

## A variational approach to nonlinear electro-magneto-elasticity: Convexity conditions and existence theorems

Miroslav Šilhavý
Mathematics and Mechanics of Solids 23 (6) 907 (2018)
DOI: 10.1177/1081286517696536

## Γ-convergence of functionals on divergence-free fields

ESAIM: Control, Optimisation and Calculus of Variations 13 (4) 809 (2007)
DOI: 10.1051/cocv:2007041

## Γ-convergence of multiscale periodic functionals depending on the time-derivative and the curl operator

Hélia Serrano
Journal of Mathematical Analysis and Applications 387 (2) 1024 (2012)
DOI: 10.1016/j.jmaa.2011.10.011

## A variational approach to the homogenization of laminate metamaterials

Hélia Serrano
Nonlinear Analysis: Real World Applications 18 75 (2014)
DOI: 10.1016/j.nonrwa.2014.01.001

## Heterogeneous Thin Films: Combining Homogenization and Dimension Reduction with Directors

Carolin Kreisbeck and Stefan Krömer
SIAM Journal on Mathematical Analysis 48 (2) 785 (2016)
DOI: 10.1137/15M1032557

## Power-Law Approximation under Differential Constraints

SIAM Journal on Mathematical Analysis 46 (2) 1085 (2014)
DOI: 10.1137/130911391

## Homogenization of layered materials with rigid components in single-slip finite crystal plasticity

Fabian Christowiak and Carolin Kreisbeck
Calculus of Variations and Partial Differential Equations 56 (3) (2017)
DOI: 10.1007/s00526-017-1171-3

## Homogenization of Functionals with Linear Growth in the Context of $$\mathcal A$$ A -quasiconvexity

José Matias, Marco Morandotti and Pedro M. Santos
Applied Mathematics & Optimization 72 (3) 523 (2015)
DOI: 10.1007/s00245-015-9289-1

## On Γ-convergence in divergence-free fields through Young measures

Hélia Serrano
Journal of Mathematical Analysis and Applications 359 (1) 311 (2009)
DOI: 10.1016/j.jmaa.2009.05.056

## Relaxation of certain integral functionals depending on strain and chemical composition

Ana Margarida Ribeiro and Elvira Zappale
Chinese Annals of Mathematics, Series B 34 (4) 491 (2013)
DOI: 10.1007/s11401-013-0784-x

## Oscillations and concentrations generated by ${\mathcal A}$-free mappings and weak lower semicontinuity of integral functionals

Irene Fonseca and Martin Kružík
ESAIM: Control, Optimisation and Calculus of Variations 16 (2) 472 (2010)
DOI: 10.1051/cocv/2009006

## Reiterated homogenization of the vector potential formulation of a magnetostatic problem in anisotropic composite media

Hélia Serrano
Nonlinear Analysis: Theory, Methods & Applications 74 (18) 7380 (2011)
DOI: 10.1016/j.na.2011.07.068

## Lower semicontinuity and relaxation of signed functionals with linear growth in the context of $${\mathcal A}$$ -quasiconvexity

Margarida Baía, Milena Chermisi, José Matias and Pedro M. Santos
Calculus of Variations and Partial Differential Equations 47 (3-4) 465 (2013)
DOI: 10.1007/s00526-012-0524-1

## Homogenization of micromagnetics large bodies

Giovanni Pisante
ESAIM: Control, Optimisation and Calculus of Variations 10 (2) 295 (2004)
DOI: 10.1051/cocv:2004008

## $\Gamma$-Convergence of Power-Law Functionals, Variational Principles in $L^{\infty},$ and Applications

Marian Bocea and Vincenzo Nesi
SIAM Journal on Mathematical Analysis 39 (5) 1550 (2008)
DOI: 10.1137/060672388

## A note on $3$d-$1$d dimension reduction with differential constraints

Carolin Kreisbeck
Discrete and Continuous Dynamical Systems - Series S 10 (1) 55 (2016)
DOI: 10.3934/dcdss.2017003

## Modélisation de films courbés non simples de second gradient

Giuliano Gargiulo, Elvira Zappale and Hamdi Zorgati
Comptes Rendus Mathematique 344 (5) 343 (2007)
DOI: 10.1016/j.crma.2007.01.018

## Homogenization problems in the calculus of variations: an overview

José Matias and Marco Morandotti
São Paulo Journal of Mathematical Sciences 9 (2) 162 (2015)
DOI: 10.1007/s40863-015-0016-2

## Young measures generated by a class of integrands: a narrow epicontinuity and applications to Homogenization

Journal de Mathématiques Pures et Appliquées 81 (12) 1277 (2002)
DOI: 10.1016/S0021-7824(02)01276-X

## Homogenization of integral energies under periodically oscillating differential constraints

Elisa Davoli and Irene Fonseca
Calculus of Variations and Partial Differential Equations 55 (3) (2016)
DOI: 10.1007/s00526-016-0988-5

## On the asymptotic behaviour of a variable exponent power law magnetostatic problem

Hélia Serrano
Applicable Analysis 97 (12) 2097 (2018)
DOI: 10.1080/00036811.2017.1359554

## Another approach to the thin-film Γ-limit of the micromagnetic free energy in the regime of small samples

Carolin Kreisbeck
Quarterly of Applied Mathematics 71 (2) 201 (2012)
DOI: 10.1090/S0033-569X-2012-01323-5

## Closed 𝓐-p quasiconvexity and variational problems with extended real-valued integrands

ESAIM: Control, Optimisation and Calculus of Variations (2018)
DOI: 10.1051/cocv/2017062

## Relaxation of Multiwell Energies in Linearized Elasticity and Applications to Nematic Elastomers

Pierluigi Cesana
Archive for Rational Mechanics and Analysis 197 (3) 903 (2010)
DOI: 10.1007/s00205-009-0283-0

## Relaxation of functionals in the space of vector-valued functions of bounded Hessian

Calculus of Variations and Partial Differential Equations 58 (1) (2019)
DOI: 10.1007/s00526-018-1452-5

## Variational Methods for Discontinuous Structures

Irene Fonseca and Giovanni Leoni
Variational Methods for Discontinuous Structures 117 (2002)
DOI: 10.1007/978-3-0348-8193-7_9

## Geometric Analysis and Nonlinear Partial Differential Equations

Bernd Kirchheim, Stefan Müller and Vladimír Šverák
Geometric Analysis and Nonlinear Partial Differential Equations 347 (2003)
DOI: 10.1007/978-3-642-55627-2_19

## Isotropic polyconvex electromagnetoelastic bodies

M Šilhavý
Mathematics and Mechanics of Solids 24 (3) 738 (2019)
DOI: 10.1177/1081286518754567

## New results on Γ-limits of integral functionals

Nadia Ansini, Gianni Dal Maso and Caterina Ida Zeppieri
Annales de l'Institut Henri Poincaré C, Analyse non linéaire 31 (1) 185 (2014)
DOI: 10.1016/j.anihpc.2013.02.005

## Homogenization of Quasi-Crystalline Functionals via Two-Scale-Cut-and-Project Convergence

Rita Ferreira, Irene Fonseca and Raghavendra Venkatraman
SIAM Journal on Mathematical Analysis 53 (2) 1785 (2021)
DOI: 10.1137/20M1341222

## 𝒜$\mathcal{A}$-quasiconvexity at the boundary and weak lower semicontinuity of integral functionals

Jan Krämer, Stefan Krömer, Martin Kružík and Gabriel Pathó
Advances in Calculus of Variations 10 (1) 49 (2017)
DOI: 10.1515/acv-2015-0009

## Quasiconvexity, Null Lagrangians, and Hardy Space Integrability Under Constant Rank Constraints

André Guerra and Bogdan Raiță
Archive for Rational Mechanics and Analysis 245 (1) 279 (2022)
DOI: 10.1007/s00205-022-01775-3

## Homogenization of high-contrast composites under differential constraints

Elisa Davoli, Martin Kružík and Valerio Pagliari
Advances in Calculus of Variations (2022)
DOI: 10.1515/acv-2022-0009