@article{AIHPC_1994__11_5_553_0,
author = {Corbo Esposito, Antonio and De Arcangelis, Riccardo},
title = {A characterization of families of function sets described by constraints on the gradient},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {553--609},
year = {1994},
publisher = {Gauthier-Villars},
volume = {11},
number = {5},
mrnumber = {1302280},
zbl = {0839.49007},
language = {en},
url = {https://www.numdam.org/item/AIHPC_1994__11_5_553_0/}
}
TY - JOUR AU - Corbo Esposito, Antonio AU - De Arcangelis, Riccardo TI - A characterization of families of function sets described by constraints on the gradient JO - Annales de l'I.H.P. Analyse non linéaire PY - 1994 SP - 553 EP - 609 VL - 11 IS - 5 PB - Gauthier-Villars UR - https://www.numdam.org/item/AIHPC_1994__11_5_553_0/ LA - en ID - AIHPC_1994__11_5_553_0 ER -
%0 Journal Article %A Corbo Esposito, Antonio %A De Arcangelis, Riccardo %T A characterization of families of function sets described by constraints on the gradient %J Annales de l'I.H.P. Analyse non linéaire %D 1994 %P 553-609 %V 11 %N 5 %I Gauthier-Villars %U https://www.numdam.org/item/AIHPC_1994__11_5_553_0/ %G en %F AIHPC_1994__11_5_553_0
Corbo Esposito, Antonio; De Arcangelis, Riccardo. A characterization of families of function sets described by constraints on the gradient. Annales de l'I.H.P. Analyse non linéaire, Tome 11 (1994) no. 5, pp. 553-609. https://www.numdam.org/item/AIHPC_1994__11_5_553_0/
[1] and , Semicontinuity Problems in the Calculus of Variations, Arch. Rational Mech. Anal., 86, 1984, pp. 125-145. | Zbl | MR
[2] , Variational Convergence for Functions and Operators, Pitman, London, 1984. | Zbl | MR
[3] and , Variational Inequalities with Varying Obstacles: The General Form of the Limit Problem, J. Funct. Anal., 50, 1983, pp. 329-386. | MR
[4] and , Disequazioni variazionali e quasivariazionali. Applicazioni a problemi di frontiera libera. Vol. 1: Problemi variazionali, Quaderni Unione Matematica Italiana, Pitagora Editrice, Bologna, 1978.
[5] , and , Asymptotic Analysis for Periodic Structures, North Holland, Amsterdam, 1978. | Zbl | MR
[6] , Integration of Functions with Values in a Banach Space, Trans. Amer. Mat. Soc., 38, 1935, pp. 357-378. | Zbl | MR | JFM
[7] , Convergence et relaxation de fonctionnelles du calcul des variations à croissance linéaire. Applications à l'homogénéisation en plasticité, Ann. Fac. Sci. Univ. Toulouse, Math., VIII, 1, 1986/87, pp. 7-36. | Zbl | MR | Numdam
[8] and , Integral Representation and Relaxation of Convex Local Functionals on BV (Ω), Ann. Sc. Norm. Sup. Pisa, IV, 20, 1993, pp. 483-533. | Zbl | MR | Numdam
[9] and , Integral Representation of Convex Functionals on a Space of Measures, J. Funct. Anal., 80, 1988, pp. 398-420. | Zbl | MR
[10] , Multiplicateur de Lagrange en torsion élastoplastique, Arch. Rational Mech. Anal., 49, 1973, pp. 32-40. | Zbl | MR
[11] and , Équivalence de deux inéquations variationnelles et applications, Arch. Rational Mech. Anal., 41, 1971, pp. 254-265. | Zbl | MR
[12] and , Sur la régularité de la solution d'inéquations elliptiques, Bull. Soc. Math. France, 96, 1968, pp. 153-180. | Zbl | MR | Numdam
[13] , Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations, Longman, Scientific & Technical, 1989. | Zbl
[14] and , Integral Representation and Relaxation of Local Functionals, Nonlinear Anal., 9, 1985, pp. 515-532. | Zbl | MR
[15] , Sur la convergence des intégrales du type de l'énergie sur des fonctions à gradient borné, J. Math. Pures Appl., 56, 9, 1977, pp. 79-84. | Zbl | MR
[16] , Γ-convergence d'intégrales sur des fonctions avec des contraintes sur le gradient, Comm. Part. Diff. Eq., 2, 1977, pp. 627-651. | Zbl | MR
[17] , Sull' omogeneizzazione di un problema variazionale con vincoli sul gradiente, Atti Accad. Naz. Lincei, Rend. Cl. Sci. Fis. Mat. Natur., 63, 8, 1977, pp. 10-14. | Zbl
[18] , Sur un problème d'homogénéisation avec des contraintes sur le gradient, J. Math. Pures Appl., 58, 1979, pp. 275-297. | Zbl | MR
[19] and , On a Problem of Homogenization with Quickly Oscillating Constraints on the Gradient, J. Math. Anal. Appl., 90, 1982, pp. 219-250. | Zbl | MR
[20] and , Further Results on a Problem of Homogenization with Constraints on the Gradient, J. Analyse Math. , 44, 1984/85, pp. 1-20. | Zbl | MR
[21] and , Homogenization with Unbounded Constraints on the Gradient, Nonlinear Anal., 9, 1985, pp. 431-444. | Zbl | MR
[22] and , Some Properties of Γ-limits of Integral Functionals, Ann. Math. Pura Appl., 122, 1979, pp. 1-60. | Zbl | MR
[23] and , Homogenization in Open Sets with Holes, J. Math. Pures Appl., 71, 1979, pp. 590-607. | Zbl | MR
[24] and , Comparison Results for Some Types of Relaxation of Variational Integral Functionals, Ann. Mat. Pura Appl., 164, 1993, pp. 155-193. | Zbl | MR
[25] and , The Lavrentieff Phenomenon and Different Processes of Homogenization, Comm. Part. Diff. Eq., 17, 1992, pp. 1503-1538. | Zbl | MR
[26] and , Homogenization of Dirichlet Problems with Nonnegative Bounded Constraints on the Gradient, to appear onJ. Analyse Math. | Zbl
[27] , Integral Representation on BV (Ω) of Γ-limits of Variational Integrals, Manuscripta Math., 30, 1980, pp. 387-413. | Zbl | MR
[28] and , A General Theory of Variational Functionals, Topics in Functional Analysis 1980/81, Quaderni della Scuola Normale Superiore, Pisa, 1982, pp 149-221. | Zbl | MR
[29] , A General Homogenization Result for Almost Periodic Functionals, J. Math. Anal. Appl., 156, 1991, pp. 358-380. | Zbl | MR
[30] and , Some Cases of Homogenization with Unbounded Oscillating Constraints on the Gradient, Asymp. Anal., 5, 1992, pp. 397-428. | Zbl | MR
[3 1 ] , Sulla convergenza di alcune successioni di integrali del tipo dell'area, Rend. Mat. Roma, 8, 1975, pp. 277-294. | Zbl | MR
[32] , Convergence Problems for Functionals and Operators, Proceed. Int. Meeting on "Recent Methods in Nonlinear Analysis", Rome 8-12 May 1975, Pitagora ed., Bologna, 1979, pp. 131-188. | Zbl | MR
[33] , and , Frontiere orientate di misura minima e questioni collegate, Quaderni della Scuola Normale Superiore, Pisa, 1972. | Zbl | MR
[34] and , Su un tipo di convergenza variazionale, Rend. Sem. Mat. Brescia, 3, 1979, pp. 63-101.
[35] and , Une notion générale de convergence faible pour des fonctions croissantes d'ensemble, Ann. Sc. Norm. Sup. Pisa, (4), 4, 1977, pp. 61-99. | Zbl | MR | Numdam
[36] and , Convex Functions of a Measure and Applications, Indiana Univ. Math. J., 33, 5, 1984, pp. 673-709. | Zbl | MR
[37] and , Linear Operators, Wiley-Interscience Publications, 1957. | Zbl
[38] and , Les Inéquations en mécanique et en physique, Dunod, Paris, 1972. | Zbl | MR
[39] and , Convex Analysis and Variational Problems, North-Holland American Elsevier, 1976. | Zbl | MR
[40] , Γ-convergenza unidimensionale, Boll. Un. Mat. Ital. B , 16-B, 1979, pp. 74-86. | Zbl | MR
[41] , Minimal Surfaces and Functions of Bounded Variations, Birkhäuser-Verlag, Basel, 1984. | Zbl | MR
[42] and , Torsion élastoplastique d'une barre cylindrique de section multiconnexe, J. Mech., 12, 1973, pp. 151-171. | Zbl | MR
[43] and , Sublinear Functions of Measures and Variational Integrals, Duke Math. J., 31, 1964, pp. 159-178. | Zbl | MR
[44] and , An Introduction to Variational Inequalities and their Applications, Academic Press, Pure and Applied Mathematics, 1980. | Zbl | MR
[45] , Topology, Academic Press, New York, 1966. | Zbl | MR
[46] , Torsion élastoplastique d'une barre cylindrique de section simplement ou multiplement connexe, J. Mech., 13, 1974, pp. 267-320. | Zbl | MR
[47] and , Homogenization of non Uniformly Elliptic Operators, Applicable Analysis, 8, 1978, pp. 101-113. | Zbl | MR
[48] , Integration in a Convex Linear Topological Space, Trans. Amer. Mat. Soc., 47, 1940, pp. 114-145. | Zbl | MR
[49] , Analisi Reale e Complessa, Boringhieri, Torino, 1980.
[50] , Su alcune applicazioni di un tipo di convergenza variazionale, Ann. Sc. Norm. Sup. Pisa, 2, 1975, pp. 617-638. | Zbl | MR | Numdam
[51] On the Definition and Properties of Certain Variational Integrals, Trans. Amer. Math. Soc., 101, 1961, pp. 139-167. | Zbl | MR
[52] , Sulla convergenza delle soluzioni di equazioni paraboliche ed ellittiche, Ann. Sc. Norm. Sup. Pisa, 22, 1968, pp. 577-597. | Zbl | MR | Numdam
[53] , Elastic-plastic Torsion, Arch. Rational Mech. Anal, 24, 1969, pp. 228-244. | Zbl | MR
