@article{AIHPC_2007__24_1_113_0,
author = {de Arcangelis, Riccardo},
title = {On the relaxation of some classes of pointwise gradient constrained energies},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {113--137},
year = {2007},
publisher = {Elsevier},
volume = {24},
number = {1},
doi = {10.1016/j.anihpc.2005.12.003},
mrnumber = {2286561},
zbl = {1112.49014},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.anihpc.2005.12.003/}
}
TY - JOUR AU - de Arcangelis, Riccardo TI - On the relaxation of some classes of pointwise gradient constrained energies JO - Annales de l'I.H.P. Analyse non linéaire PY - 2007 SP - 113 EP - 137 VL - 24 IS - 1 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.anihpc.2005.12.003/ DO - 10.1016/j.anihpc.2005.12.003 LA - en ID - AIHPC_2007__24_1_113_0 ER -
%0 Journal Article %A de Arcangelis, Riccardo %T On the relaxation of some classes of pointwise gradient constrained energies %J Annales de l'I.H.P. Analyse non linéaire %D 2007 %P 113-137 %V 24 %N 1 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.anihpc.2005.12.003/ %R 10.1016/j.anihpc.2005.12.003 %G en %F AIHPC_2007__24_1_113_0
de Arcangelis, Riccardo. On the relaxation of some classes of pointwise gradient constrained energies. Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 1, pp. 113-137. doi: 10.1016/j.anihpc.2005.12.003
[1] , Variational Convergence for Functions and Operators, Pitman, London, 1984. | Zbl | MR
[2] , Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations, Pitman Res. Notes Math. Ser., vol. 207, Longman Scientific & Technical, Harlow, 1989. | Zbl | MR
[3] , , , , Homogenization of unbounded functionals and nonlinear elastomers. The case of the fixed constraints set, ESAIM Control Optim. Calc. Var. 10 (2004) 53-83. | Zbl | MR | Numdam
[4] , , , Homogenization of Neumann problems for unbounded functionals, Boll. Un. Mat. Ital. Sez. B Artic. Ric. Mat. 2-B (8) (1999) 463-491. | Zbl | MR
[5] , , On the relaxation of some classes of unbounded integral functionals, Matematiche 51 (1996) 221-256, (special issue in Honour of Francesco Guglielmino). | Zbl | MR
[6] , , On the relaxation of Dirichlet minimum problems for some classes of unbounded integral functionals, Ricerche Mat. 48 (Suppl.) (1999) 347-372, (special issue in memory of Ennio De Giorgi). | Zbl | MR
[7] , , On a non-standard convex regularization and the relaxation of unbounded functionals of the calculus of variations, J. Convex Anal. 6 (1999) 141-162. | Zbl | MR
[8] , , Unbounded Functionals in the Calculus of Variations. Representation, Relaxation, and Homogenization, Chapman & Hall/CRC Monogr. Surv. Pure Appl. Math., vol. 125, Chapman & Hall/CRC, Boca Raton, FL, 2001. | Zbl | MR
[9] , , Some properties of Γ-limits of integral functionals, Ann. Mat. Pura Appl. (4) 122 (1979) 1-60. | Zbl
[10] , , Comparison results for some types of relaxation of variational integral functionals, Ann. Mat. Pura Appl. (4) 164 (1993) 155-193. | Zbl | MR
[11] , Direct Methods in the Calculus of Variations, Appl. Math. Sci., vol. 78, Springer, Berlin, 1989. | Zbl | MR
[12] , , General existence theorems for Hamilton-Jacobi equations in the scalar and vectorial cases, Acta Math. 178 (1997) 1-37. | Zbl
[13] , , Implicit Partial Differential Equations, Progr. Nonlinear Differential Equations Appl., vol. 37, Birkhäuser, Boston, 1999. | Zbl | MR
[14] , An Introduction to Γ-Convergence, Progr. Nonlinear Differential Equations Appl., vol. 8, Birkhäuser, Boston, 1993. | Zbl
[15] , , , On the relaxation and the Lavrentieff phenomenon for variational integrals with pointwise measurable gradient constraints, Calc. Var. Partial Differential Equations 21 (2004) 357-400. | Zbl | MR
[16] , , On the relaxation of some classes of Dirichlet minimum problems, Comm. Partial Differential Equations 24 (1999) 975-1006. | Zbl | MR
[17] , , On the relaxation of variational integrals with pointwise continuous-type gradient constraints, Appl. Math. Optim. 51 (2005) 251-277. | Zbl | MR
[18] , , Homogenization of Dirichlet problems for some types of integral functionals, Ricerche Mat. 46 (1997) 177-202. | Zbl | MR
[19] , , Inequalities in Mechanics and Physics, Grundlehren Math. Wiss., vol. 219, Springer, Berlin, 1976. | Zbl | MR
[20] , , Convex Analysis and Variational Problems, Stud. Math. Appl., vol. 1, North-Holland, Amsterdam, 1976. | Zbl | MR
[21] , , Measure Theory and Fine Properties of Functions, Stud. Adv. Math., vol. 5, CRC Press, Boca Raton, FL, 1992. | Zbl | MR
[22] , , , Functionals with linear growth in the calculus of variations, Comment. Math. Univ. Carolin. 20 (1979) 143-156. | Zbl | MR
[23] , , Sublinear functions of measures and variational integrals, Duke Math. J. 31 (1964) 159-178. | Zbl | MR
[24] , Relaxation of multidimensional variational problems with constraints of general form, Nonlinear Anal. 45 (2001) 651-659. | Zbl | MR
[25] , , Relaxation in an -optimization problem, Proc. Roy. Soc. Edinburgh Sect. A 133 (2003) 599-615. | Zbl | MR
[26] , , Relaxation of Hamilton-Jacobi equations, Arch. Rational Mech. Anal. 169 (2003) 265-304. | Zbl
[27] , On a family of torsional creep problems, J. Reine Angew. Math. 410 (1990) 1-22. | Zbl | MR
[28] , , An Introduction to Variational Inequalities and Their Applications, Pure Appl. Math., vol. 88, Academic Press, New York, 1980. | Zbl | MR
[29] , Generalized Solutions of Hamilton-Jacobi Equations, Pitman Res. Notes Math. Ser., vol. 69, Longman Scientific & Technical, Harlow, 1982. | Zbl
[30] , , Semicontinuity problems in the calculus of variations, Nonlinear Anal. 4 (1980) 241-257. | Zbl | MR
[31] , Multiple Integrals in the Calculus of Variations, Grundlehren Math. Wiss., vol. 130, Springer, Berlin, 1966. | Zbl | MR
[32] , Convex Analysis, Princeton Math. Ser., vol. 28, Princeton University Press, Princeton, 1972. | Zbl
[33] , , Variational Analysis, Grundlehren Math. Wiss., vol. 317, Springer, Berlin, 1998. | Zbl | MR
[34] , Elastic-plastic torsion of simply connected cylindrical bars, Indiana Univ. Math. J. 20 (1971) 1047-1076. | Zbl | MR
[35] , The Physics of Rubber Elasticity, Clarendon Press, Oxford, 1975.
[36] , Weakly Differentiable Functions, Grad. Texts in Math., vol. 120, Springer, Berlin, 1989. | Zbl | MR
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