A-Quasiconvexity: Relaxation and Homogenization
ESAIM: COCV, 5 (2000) 539-577
Published online: 2002-08-15
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Junction in a thin multi-domain for nonsimple grade two materials in BH
Rita Ferreira, José Matias and Elvira ZappaleNonlinear Analysis: Real World Applications 84 104322 (2025)
https://doi.org/10.1016/j.nonrwa.2025.104322
7 91 (2024)
https://doi.org/10.1007/978-3-031-53740-0_6
Homogenization of supremal functionals in the vectorial case (via Lp-approximation)
Lorenza D’Elia, Michela Eleuteri and Elvira ZappaleAnalysis and Applications 22 (07) 1255 (2024)
https://doi.org/10.1142/S0219530524500179
Homogenization of high-contrast composites under differential constraints
Elisa Davoli, Martin Kružík and Valerio PagliariAdvances in Calculus of Variations 17 (2) 277 (2024)
https://doi.org/10.1515/acv-2022-0009
Existence of minimisers of variational problems posed in spaces of mixed smoothness
Adam ProsinskiCalculus of Variations and Partial Differential Equations 62 (1) (2023)
https://doi.org/10.1007/s00526-022-02342-0
$${\mathcal {A}}$$-Variational Principles
Luís Bandeira and Pablo PedregalMilan Journal of Mathematics 91 (2) 293 (2023)
https://doi.org/10.1007/s00032-023-00382-5
Shape optimization of light structures and the vanishing mass conjecture
Jean-François Babadjian, Flaviana Iurlano and Filip RindlerDuke Mathematical Journal 172 (1) (2023)
https://doi.org/10.1215/00127094-2022-0031
Homogenisation of dynamical optimal transport on periodic graphs
Peter Gladbach, Eva Kopfer, Jan Maas and Lorenzo PortinaleCalculus of Variations and Partial Differential Equations 62 (5) (2023)
https://doi.org/10.1007/s00526-023-02472-z
Quasiconvexity, Null Lagrangians, and Hardy Space Integrability Under Constant Rank Constraints
André Guerra and Bogdan RaițăArchive for Rational Mechanics and Analysis 245 (1) 279 (2022)
https://doi.org/10.1007/s00205-022-01775-3
Homogenization of Quasi-Crystalline Functionals via Two-Scale-Cut-and-Project Convergence
Rita Ferreira, Irene Fonseca and Raghavendra VenkatramanSIAM Journal on Mathematical Analysis 53 (2) 1785 (2021)
https://doi.org/10.1137/20M1341222
Geometric linearization of theories for incompressible elastic materials and applications
Martin Jesenko and Bernd SchmidtMathematical Models and Methods in Applied Sciences 31 (04) 829 (2021)
https://doi.org/10.1142/S0218202521500202
Generalized Multiscale Young Measures
Adolfo Arroyo-Rabasa and Johannes DiermeierSIAM Journal on Mathematical Analysis 52 (4) 3252 (2020)
https://doi.org/10.1137/19M1238848
Asymptotic Rigidity of Layered Structures and Its Application in Homogenization Theory
Fabian Christowiak and Carolin KreisbeckArchive for Rational Mechanics and Analysis 235 (1) 51 (2020)
https://doi.org/10.1007/s00205-019-01418-0
Applied Mathematical Analysis: Theory, Methods, and Applications
Hélia SerranoStudies in Systems, Decision and Control, Applied Mathematical Analysis: Theory, Methods, and Applications 177 233 (2020)
https://doi.org/10.1007/978-3-319-99918-0_8
Relaxation of functionals in the space of vector-valued functions of bounded Hessian
Adrian HagertyCalculus of Variations and Partial Differential Equations 58 (1) (2019)
https://doi.org/10.1007/s00526-018-1452-5
Isotropic polyconvex electromagnetoelastic bodies
M ŠilhavýMathematics and Mechanics of Solids 24 (3) 738 (2019)
https://doi.org/10.1177/1081286518754567
On the asymptotic behaviour of a variable exponent power law magnetostatic problem
Hélia SerranoApplicable Analysis 97 (12) 2097 (2018)
https://doi.org/10.1080/00036811.2017.1359554
A variational approach to nonlinear electro-magneto-elasticity: Convexity conditions and existence theorems
Miroslav ŠilhavýMathematics and Mechanics of Solids 23 (6) 907 (2018)
https://doi.org/10.1177/1081286517696536
Closed 𝓐-p quasiconvexity and variational problems with extended real-valued integrands
Adam ProsinskiESAIM: Control, Optimisation and Calculus of Variations (2018)
https://doi.org/10.1051/cocv/2017062
Polyconvexity for functions of a system of closed differential forms
M. ŠilhavýCalculus of Variations and Partial Differential Equations 57 (1) (2018)
https://doi.org/10.1007/s00526-017-1298-2
𝒜$\mathcal{A}$-quasiconvexity at the boundary and weak lower semicontinuity of integral functionals
Jan Krämer, Stefan Krömer, Martin Kružík and Gabriel PathóAdvances in Calculus of Variations 10 (1) 49 (2017)
https://doi.org/10.1515/acv-2015-0009
Homogenization of layered materials with rigid components in single-slip finite crystal plasticity
Fabian Christowiak and Carolin KreisbeckCalculus of Variations and Partial Differential Equations 56 (3) (2017)
https://doi.org/10.1007/s00526-017-1171-3
Weak Lower Semicontinuity of Integral Functionals and Applications
Barbora Benešová and Martin KružíkSIAM Review 59 (4) 703 (2017)
https://doi.org/10.1137/16M1060947
Michell trusses in two dimensions as a $$\Gamma $$ Γ -limit of optimal design problems in linear elasticity
Heiner OlbermannCalculus of Variations and Partial Differential Equations 56 (6) (2017)
https://doi.org/10.1007/s00526-017-1266-x
A note on $3$d-$1$d dimension reduction with differential constraints
Carolin KreisbeckDiscrete & Continuous Dynamical Systems - S 10 (1) 55 (2017)
https://doi.org/10.3934/dcdss.2017003
Heterogeneous Thin Films: Combining Homogenization and Dimension Reduction with Directors
Carolin Kreisbeck and Stefan KrömerSIAM Journal on Mathematical Analysis 48 (2) 785 (2016)
https://doi.org/10.1137/15M1032557
Homogenization of integral energies under periodically oscillating differential constraints
Elisa Davoli and Irene FonsecaCalculus of Variations and Partial Differential Equations 55 (3) (2016)
https://doi.org/10.1007/s00526-016-0988-5
Homogenization of Functionals with Linear Growth in the Context of $$\mathcal A$$ A -quasiconvexity
José Matias, Marco Morandotti and Pedro M. SantosApplied Mathematics & Optimization 72 (3) 523 (2015)
https://doi.org/10.1007/s00245-015-9289-1
Homogenization problems in the calculus of variations: an overview
José Matias and Marco MorandottiSão Paulo Journal of Mathematical Sciences 9 (2) 162 (2015)
https://doi.org/10.1007/s40863-015-0016-2
A variational approach to the homogenization of laminate metamaterials
Hélia SerranoNonlinear Analysis: Real World Applications 18 75 (2014)
https://doi.org/10.1016/j.nonrwa.2014.01.001
Power-Law Approximation under Differential Constraints
Nadia Ansini and Francesca PrinariSIAM Journal on Mathematical Analysis 46 (2) 1085 (2014)
https://doi.org/10.1137/130911391
New results on Γ-limits of integral functionals
Caterina Ida Zeppieri, Nadia Ansini and Gianni Dal MasoAnnales de l'Institut Henri Poincaré C, Analyse non linéaire 31 (1) 185 (2014)
https://doi.org/10.1016/j.anihpc.2013.02.005
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. SantosCalculus of Variations and Partial Differential Equations 47 (3-4) 465 (2013)
https://doi.org/10.1007/s00526-012-0524-1
Relaxation of certain integral functionals depending on strain and chemical composition
Ana Margarida Ribeiro and Elvira ZappaleChinese Annals of Mathematics, Series B 34 (4) 491 (2013)
https://doi.org/10.1007/s11401-013-0784-x
Another approach to the thin-film Γ-limit of the micromagnetic free energy in the regime of small samples
Carolin KreisbeckQuarterly of Applied Mathematics 71 (2) 201 (2012)
https://doi.org/10.1090/S0033-569X-2012-01323-5
Γ-convergence of multiscale periodic functionals depending on the time-derivative and the curl operator
Hélia SerranoJournal of Mathematical Analysis and Applications 387 (2) 1024 (2012)
https://doi.org/10.1016/j.jmaa.2011.10.011
Reiterated homogenization of the vector potential formulation of a magnetostatic problem in anisotropic composite media
Hélia SerranoNonlinear Analysis: Theory, Methods & Applications 74 (18) 7380 (2011)
https://doi.org/10.1016/j.na.2011.07.068
Relaxation of Multiwell Energies in Linearized Elasticity and Applications to Nematic Elastomers
Pierluigi CesanaArchive for Rational Mechanics and Analysis 197 (3) 903 (2010)
https://doi.org/10.1007/s00205-009-0283-0
Oscillations and concentrations generated by ${\mathcal A}$-free mappings and weak lower semicontinuity of integral functionals
Irene Fonseca and Martin KružíkESAIM: Control, Optimisation and Calculus of Variations 16 (2) 472 (2010)
https://doi.org/10.1051/cocv/2009006
On Γ-convergence in divergence-free fields through Young measures
Hélia SerranoJournal of Mathematical Analysis and Applications 359 (1) 311 (2009)
https://doi.org/10.1016/j.jmaa.2009.05.056
$\Gamma$-Convergence of Power-Law Functionals, Variational Principles in $L^{\infty},$ and Applications
Marian Bocea and Vincenzo NesiSIAM Journal on Mathematical Analysis 39 (5) 1550 (2008)
https://doi.org/10.1137/060672388
Modélisation de films courbés non simples de second gradient
Giuliano Gargiulo, Elvira Zappale and Hamdi ZorgatiComptes Rendus. Mathématique 344 (5) 343 (2007)
https://doi.org/10.1016/j.crma.2007.01.018
Γ-convergence of functionals on divergence-free fields
Nadia Ansini and Adriana GarroniESAIM: Control, Optimisation and Calculus of Variations 13 (4) 809 (2007)
https://doi.org/10.1051/cocv:2007041
Relaxation and Γ-Convergence of the Energy Functionals of a Two-Phase Elastic Medium
A. V. Dem’yanovJournal of Mathematical Sciences 128 (5) 3177 (2005)
https://doi.org/10.1007/s10958-005-0263-3
Homogenization of micromagnetics large bodies
Giovanni PisanteESAIM: Control, Optimisation and Calculus of Variations 10 (2) 295 (2004)
https://doi.org/10.1051/cocv:2004008
A -quasiconvexity: weak-star convergence and the gap
Irene Fonseca, Giovanni Leoni and Stefan MüllerAnnales de l'Institut Henri Poincare (C) Non Linear Analysis 21 (2) 209 (2004)
https://doi.org/10.1016/j.anihpc.2003.01.003
Geometric Analysis and Nonlinear Partial Differential Equations
Bernd Kirchheim, Stefan Müller and Vladimír ŠverákGeometric Analysis and Nonlinear Partial Differential Equations 347 (2003)
https://doi.org/10.1007/978-3-642-55627-2_19
Variational Methods for Discontinuous Structures
Irene Fonseca and Giovanni LeoniVariational Methods for Discontinuous Structures 117 (2002)
https://doi.org/10.1007/978-3-0348-8193-7_9
Young measures generated by a class of integrands: a narrow epicontinuity and applications to Homogenization
Gérard Michaille and Michel ValadierJournal de Mathématiques Pures et Appliquées 81 (12) 1277 (2002)
https://doi.org/10.1016/S0021-7824(02)01276-X