A-quasiconvexity : weak-star convergence and the gap
Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) no. 2, pp. 209-236.
@article{AIHPC_2004__21_2_209_0,
     author = {Fonseca, Irene and Leoni, Giovanni and M\"uller, Stefan},
     title = {A-quasiconvexity : weak-star convergence and the gap},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {209--236},
     publisher = {Elsevier},
     volume = {21},
     number = {2},
     year = {2004},
     doi = {10.1016/j.anihpc.2003.01.003},
     mrnumber = {2021666},
     zbl = {1064.49016},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2003.01.003/}
}
TY  - JOUR
AU  - Fonseca, Irene
AU  - Leoni, Giovanni
AU  - Müller, Stefan
TI  - A-quasiconvexity : weak-star convergence and the gap
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2004
SP  - 209
EP  - 236
VL  - 21
IS  - 2
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.anihpc.2003.01.003/
DO  - 10.1016/j.anihpc.2003.01.003
LA  - en
ID  - AIHPC_2004__21_2_209_0
ER  - 
%0 Journal Article
%A Fonseca, Irene
%A Leoni, Giovanni
%A Müller, Stefan
%T A-quasiconvexity : weak-star convergence and the gap
%J Annales de l'I.H.P. Analyse non linéaire
%D 2004
%P 209-236
%V 21
%N 2
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.anihpc.2003.01.003/
%R 10.1016/j.anihpc.2003.01.003
%G en
%F AIHPC_2004__21_2_209_0
Fonseca, Irene; Leoni, Giovanni; Müller, Stefan. A-quasiconvexity : weak-star convergence and the gap. Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) no. 2, pp. 209-236. doi : 10.1016/j.anihpc.2003.01.003. https://www.numdam.org/articles/10.1016/j.anihpc.2003.01.003/

[1] E. Acerbi, G. Bouchitté, I. Fonseca, Relaxation of convex functionals and the Lavrentiev phenomenon, submitted for publication.

[2] Acerbi E., Buttazzo G., Fusco N., Semicontinuity and relaxation for integrals depending on vector valued functions, J. Math. Pures Appl. 62 (1983) 371-387. | MR | Zbl

[3] Acerbi E., Dal Maso G., New lower semicontinuity results for polyconvex integrals case, Calc. Var. 2 (1994) 329-372. | MR | Zbl

[4] Acerbi E., Fusco N., Semicontinuity problems in the calculus of variations, Arch. Rational Mech. Anal. 86 (1984) 125-145. | MR | Zbl

[5] Ambrosio L., Fusco N., Pallara D., Functions of Bounded Variation and Free Discontinuity Problems, Mathematical Monographs, Oxford University Press, 2000. | MR | Zbl

[6] Ambrosio L., Dal Maso G., On the relaxation in BV(Ω;Rm) of quasi-convex integrals, J. Funct. Anal. 109 (1992) 76-97. | Zbl

[7] Ball J., Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63 (1977) 337-403. | MR | Zbl

[8] Ball J.M., Murat F., W1,p quasiconvexity and variational problems for multiple integrals, J. Funct. Anal. 58 (1984) 225-253. | MR | Zbl

[9] Bouchitté G., Fonseca I., Malý J., Relaxation of multiple integrals below the growth exponent, Proc. Roy. Soc. Edinburgh Sect. A 128 (1998) 463-479. | MR | Zbl

[10] Braides A., Fonseca I., Leoni G., A-quasiconvexity: relaxation and homogenization, ESAIM:COCV 5 (2000) 539-577. | Numdam | MR | Zbl

[11] Burenkov V.I., Sobolev Spaces on Domains, Teuber, Stuttgart, 1998. | MR | Zbl

[12] Celada P., Dal Maso G., Further remarks on the lower semicontinuity of polyconvex integrals, Ann. Inst. H. Poincaré Anal. Non Linéaire 11 (1994) 661-691. | Numdam | MR | Zbl

[13] Dacorogna B., Weak Continuity and Weak Lower Semicontinuity for Nonlinear Functionals, Lecture Notes in Mathem., vol. 922, Springer, Berlin, 1982. | MR | Zbl

[14] Dacorogna B., Direct Methods in the Calculus of Variations, Springer, New York, 1989. | MR | Zbl

[15] Dal Maso G., Sbordone C., Weak lower semicontinuity of polyconvex integrals: a borderline case, Math. Z. 218 (1995) 603-609. | MR | Zbl

[16] De Simone A., Energy minimizers for large ferromagnetic bodies, Arch. Rational Mech. Anal. 125 (1993) 99-143. | MR | Zbl

[17] Demengel F., Fonctions à hessien borné, Ann. Inst. Fourier 34 (1984) 155-190. | Numdam | MR | Zbl

[18] L. Esposito, F. Leonetti, G. Mingione, Sharp regularity for functionals with (p,q) growth, Preprint. | MR

[19] L. Esposito, G. Mingione, Relaxation results for higher order integrals below the natural growth exponent, Differential Integral Equations, submitted for publication. | MR | Zbl

[20] I. Fonseca, G. Leoni, J. Malý, Weak continuity and lower semicontinuity results for determinants, in preparation.

[21] Fonseca I., Malý J., Relaxation of multiple integrals below the growth exponent, Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (1997) 308-338. | Numdam | MR | Zbl

[22] Fonseca I., Marcellini P., Relaxation of multiple integrals in subcritical Sobolev spaces, J. Geom. Anal. 7 (1997) 57-81. | MR | Zbl

[23] Fonseca I., Müller S., Quasiconvex integrands and lower semicontinuity in L1, SIAM J. Math. Anal. 23 (1992) 1081-1098. | MR | Zbl

[24] Fonseca I., Müller S., Relaxation of quasiconvex functionals in BV(Ω, Rp) for integrands f(x,u,∇u), Arch. Rational Mech. Anal. 123 (1993) 1-49. | Zbl

[25] Fonseca I., Müller S., A-quasiconvexity, lower semicontinuity and Young measures, SIAM J. Math. Anal. 30 (1999) 1355-1390. | MR | Zbl

[26] Gagliardo E., Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in n variabili, Rend. Sem. Mat. Padova 27 (1957) 283-305. | Numdam | MR | Zbl

[27] Gangbo W., On the weak lower semicontinuity of energies with polyconvex integrands, J. Math. Pures Appl. 73 (1994) 455-469. | MR | Zbl

[28] Guidorzi M., Poggiolini L., Lower semicontinuity for quasiconvex integrals of higher order, Nonlinear Differential Equations Appl. 6 (1999) 227-246. | MR | Zbl

[29] Kristensen J., Lower semicontinuity of quasi-convex integrands in BV, Calc. Var. 7 (1998) 249-261. | MR | Zbl

[30] Malý J., Weak lower semicontinuity of polyconvex integrals, Proc. Roy. Soc. Edinburgh Sect. A 123 (1993) 681-691. | MR | Zbl

[31] Malý J., Lower semicontinuity of quasiconvex integrals, Manuscripta Math. 85 (1994) 419-428. | MR | Zbl

[32] Marcellini P., Approximation of quasiconvex functions and lower semicontinuity of multiple integrals quasiconvex integrals, Manuscripta Math. 51 (1985) 1-28. | MR | Zbl

[33] Marcellini P., On the definition and the lower semicontinuity of certain quasiconvex integrals, Ann. Inst. H. Poincaré Anal. Non Linéaire 3 (1986) 391-409. | Numdam | MR | Zbl

[34] Maz'Ja V.G., Sobolev Spaces, Springer, Berlin, 1985. | MR

[35] Meyers N.G., Quasi-convexity and lower semi-continuity of multiple variational integrals of any order, Trans. Amer. Math. Soc. 119 (1965) 125-149. | MR | Zbl

[36] Morrey C.B., Multiple Integrals in the Calculus of Variations, Springer, Berlin, 1966. | MR | Zbl

[37] Murat F., Compacité par compensation : condition necessaire et suffisante de continuité faible sous une hypothése de rang constant, Ann. Sc. Norm. Sup. Pisa 8 (4) (1981) 68-102. | Numdam | MR | Zbl

[38] Pedregal P., Parametrized Measures and Variational Principles, Birkhäuser, Boston, 1997. | MR | Zbl

[39] P. Santos, E. Zappale, in preparation.

[40] Serrin J., On the definition and properties of certain variational integrals, Trans. Amer. Math. Soc. 161 (1961) 139-167. | MR | Zbl

[41] Stein E.M., Harmonic Analysis, Princeton University Press, 1993. | MR | Zbl

[42] Tartar L., Compensated compactness and applications to partial differential equations, in: Knops R. (Ed.), Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, vol. IV, Res. Notes Math., vol. 39, Pitman, 1979, pp. 136-212. | MR | Zbl

[43] Tartar L., The compensated compactness method applied to systems of conservation laws, in: Ball J.M. (Ed.), Systems of Nonlinear Partial Differential Eq., Riedel, 1983. | MR | Zbl

[44] Tartar L., Étude des oscillations dans les équations aux dérivées partielles nonlinéaires, in: Lecture Notes in Phys., vol. 195, Springer, Berlin, 1984, pp. 384-412. | MR | Zbl

[45] Tartar L., H-measures, a new approach for studying homogenisation, oscillations and concentration effects in partial differential equations, Proc. Roy. Soc. Edinburgh Sect. A 115 (1990) 193-230. | MR | Zbl

[46] Tartar L., On mathematical tools for studying partial differential equations of continuum physics: H-measures and Young measures, in: Buttazzo , Galdi , Zanghirati (Eds.), Developments in Partial Differential Equations and Applications to Mathematical Physics, Plenum, New York, 1991. | MR | Zbl

[47] Tartar L., Some remarks on separately convex functions, in: Kinderlehrer D., James R.D., Luskin M., Ericksen J.L. (Eds.), Microstructure and Phase Transitions, IMA Vol. Math. Appl., vol. 54, Springer, Berlin, 1993, pp. 191-204. | MR | Zbl

[48] Zhikov V.V., On Lavrentiev's phenomenon, Russian J. Math. Phys. 3 (1995) 249-269. | MR | Zbl

[49] Zhikov V.V., On some variational problems, Russian J. Math. Phys. 5 (1997) 105-116. | MR | Zbl

  • Almi, Stefano; Reggiani, Dario; Solombrino, Francesco Lower semicontinuity and relaxation for free discontinuity functionals with non-standard growth, Calculus of Variations and Partial Differential Equations, Volume 63 (2024) no. 1 | DOI:10.1007/s00526-023-02623-2
  • Prosinski, Adam Existence of minimisers of variational problems posed in spaces of mixed smoothness, Calculus of Variations and Partial Differential Equations, Volume 62 (2023) no. 1 | DOI:10.1007/s00526-022-02342-0
  • Bandeira, Luís; Pedregal, Pablo A-Variational Principles, Milan Journal of Mathematics, Volume 91 (2023) no. 2, p. 293 | DOI:10.1007/s00032-023-00382-5
  • Olbermann, Heiner Michell truss type theories as a Γ-limit of optimal design in linear elasticity, Advances in Calculus of Variations, Volume 15 (2022) no. 3, p. 305 | DOI:10.1515/acv-2019-0074
  • Guerra, André; Raiță, Bogdan Quasiconvexity, Null Lagrangians, and Hardy Space Integrability Under Constant Rank Constraints, Archive for Rational Mechanics and Analysis, Volume 245 (2022) no. 1, p. 279 | DOI:10.1007/s00205-022-01775-3
  • Arroyo-Rabasa, Adolfo Characterization of Generalized Young Measures Generated by A-free Measures, Archive for Rational Mechanics and Analysis, Volume 242 (2021) no. 1, p. 235 | DOI:10.1007/s00205-021-01683-y
  • Arroyo-Rabasa, Adolfo; De Philippis, Guido; Rindler, Filip Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints, Advances in Calculus of Variations, Volume 13 (2020) no. 3, p. 219 | DOI:10.1515/acv-2017-0003
  • De Rosa, Luigi; Serre, Denis; Tione, Riccardo On the upper semicontinuity of a quasiconcave functional, Journal of Functional Analysis, Volume 279 (2020) no. 7, p. 108660 | DOI:10.1016/j.jfa.2020.108660
  • Sil, Swarnendu Calculus of variations: A differential form approach, Advances in Calculus of Variations, Volume 12 (2019) no. 1, p. 57 | DOI:10.1515/acv-2016-0058
  • Prosinski, Adam Closed 𝓐-pQuasiconvexity and Variational Problems with Extended Real-Valued Integrands, ESAIM: Control, Optimisation and Calculus of Variations, Volume 24 (2018) no. 4, p. 1605 | DOI:10.1051/cocv/2017062
  • Davoli, Elisa; Fonseca, Irene Relaxation of p-Growth Integral Functionals Under Space-Dependent Differential Constraints, Trends in Applications of Mathematics to Mechanics, Volume 27 (2018), p. 1 | DOI:10.1007/978-3-319-75940-1_1
  • Krämer, Jan; Krömer, Stefan; Kružík, Martin; Pathó, Gabriel 𝒜A-quasiconvexity at the boundary and weak lower semicontinuity of integral functionals, Advances in Calculus of Variations, Volume 10 (2017) no. 1, p. 49 | DOI:10.1515/acv-2015-0009
  • Ferreira, Rita; Fonseca, Irene; Mascarenhas, M. Luísa A chromaticity-brightness model for color images denoising in a Meyer’s “u + v” framework, Calculus of Variations and Partial Differential Equations, Volume 56 (2017) no. 5 | DOI:10.1007/s00526-017-1223-8
  • Kreisbeck, Carolin A note on 3d-1d dimension reduction with differential constraints, Discrete Continuous Dynamical Systems - S, Volume 10 (2017) no. 1, p. 55 | DOI:10.3934/dcdss.2017003
  • Cherednichenko, K. D.; Cooper, S.; Guenneau, S. Spectral Analysis of One-Dimensional High-Contrast Elliptic Problems with Periodic Coefficients, Multiscale Modeling Simulation, Volume 13 (2015) no. 1, p. 72 | DOI:10.1137/130947106
  • Kristensen, Jan A necessary and sufficient condition for lower semicontinuity, Nonlinear Analysis: Theory, Methods Applications, Volume 120 (2015), p. 43 | DOI:10.1016/j.na.2015.02.018
  • Baía, Margarida; Chermisi, Milena; Matias, José; Santos, Pedro M. Lower semicontinuity and relaxation of signed functionals with linear growth in the context of A -quasiconvexity, Calculus of Variations and Partial Differential Equations, Volume 47 (2013) no. 3-4, p. 465 | DOI:10.1007/s00526-012-0524-1
  • Soneji, Parth Lower semicontinuity in BV of quasiconvex integrals with subquadratic growth, ESAIM: Control, Optimisation and Calculus of Variations, Volume 19 (2013) no. 2, p. 555 | DOI:10.1051/cocv/2012021
  • Giannetti, Flavia Lower semicontinuity for higher order integrals below the growth exponent, Manuscripta Mathematica, Volume 136 (2011) no. 1-2, p. 143 | DOI:10.1007/s00229-011-0434-0

Cité par 19 documents. Sources : Crossref