On the relaxation of some classes of pointwise gradient constrained energies
de Arcangelis, Riccardo
Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007), p. 113-137 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@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},
     volume = {24},
     year = {2007},
     pages = {113-137},
     doi = {10.1016/j.anihpc.2005.12.003},
     mrnumber = {2286561},
     zbl = {1112.49014},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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) pp. 113-137. doi : 10.1016/j.anihpc.2005.12.003. http://gdmltest.u-ga.fr/item/AIHPC_2007__24_1_113_0/

[1] Attouch H., Variational Convergence for Functions and Operators, Pitman, London, 1984. | MR 773850 | Zbl 0561.49012

[2] Buttazzo G., Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations, Pitman Res. Notes Math. Ser., vol. 207, Longman Scientific & Technical, Harlow, 1989. | MR 1020296 | Zbl 0669.49005

[3] Carbone L., Cioranescu D., De Arcangelis R., Gaudiello A., Homogenization of unbounded functionals and nonlinear elastomers. The case of the fixed constraints set, ESAIM Control Optim. Calc. Var. 10 (2004) 53-83. | Numdam | MR 2084255 | Zbl 1072.49008

[4] Carbone L., Corbo Esposito A., De Arcangelis R., Homogenization of Neumann problems for unbounded functionals, Boll. Un. Mat. Ital. Sez. B Artic. Ric. Mat. 2-B (8) (1999) 463-491. | MR 1706544 | Zbl 0940.49015

[5] Carbone L., De Arcangelis R., On the relaxation of some classes of unbounded integral functionals, Matematiche 51 (1996) 221-256, (special issue in Honour of Francesco Guglielmino). | MR 1488070 | Zbl 0908.49012

[6] Carbone L., De Arcangelis R., 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). | MR 1765692 | Zbl 0941.49008

[7] Carbone L., De Arcangelis R., On a non-standard convex regularization and the relaxation of unbounded functionals of the calculus of variations, J. Convex Anal. 6 (1999) 141-162. | MR 1713955 | Zbl 0940.49016

[8] Carbone L., De Arcangelis R., 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. | MR 1910459 | Zbl 1002.49018

[9] Carbone L., Sbordone C., Some properties of Γ-limits of integral functionals, Ann. Mat. Pura Appl. (4) 122 (1979) 1-60. | Zbl 0474.49016

[10] Corbo Esposito A., De Arcangelis R., Comparison results for some types of relaxation of variational integral functionals, Ann. Mat. Pura Appl. (4) 164 (1993) 155-193. | MR 1243954 | Zbl 0931.49009

[11] Dacorogna B., Direct Methods in the Calculus of Variations, Appl. Math. Sci., vol. 78, Springer, Berlin, 1989. | MR 990890 | Zbl 0703.49001

[12] Dacorogna B., Marcellini P., General existence theorems for Hamilton-Jacobi equations in the scalar and vectorial cases, Acta Math. 178 (1997) 1-37. | Zbl 0901.49027

[13] Dacorogna B., Marcellini P., Implicit Partial Differential Equations, Progr. Nonlinear Differential Equations Appl., vol. 37, Birkhäuser, Boston, 1999. | MR 1702252 | Zbl 0938.35002

[14] Dal Maso G., An Introduction to Γ-Convergence, Progr. Nonlinear Differential Equations Appl., vol. 8, Birkhäuser, Boston, 1993. | Zbl 0816.49001

[15] De Arcangelis R., Monsurrò S., Zappale E., On the relaxation and the Lavrentieff phenomenon for variational integrals with pointwise measurable gradient constraints, Calc. Var. Partial Differential Equations 21 (2004) 357-400. | MR 2098073 | Zbl 1062.49012

[16] De Arcangelis R., Trombetti C., On the relaxation of some classes of Dirichlet minimum problems, Comm. Partial Differential Equations 24 (1999) 975-1006. | MR 1680889 | Zbl 0928.49014

[17] De Arcangelis R., Zappale E., On the relaxation of variational integrals with pointwise continuous-type gradient constraints, Appl. Math. Optim. 51 (2005) 251-277. | MR 2148926 | Zbl 1100.49015

[18] De Maio U., Durante T., Homogenization of Dirichlet problems for some types of integral functionals, Ricerche Mat. 46 (1997) 177-202. | MR 1615758 | Zbl 0945.49006

[19] Duvaut G., Lions J.-L., Inequalities in Mechanics and Physics, Grundlehren Math. Wiss., vol. 219, Springer, Berlin, 1976. | MR 521262 | Zbl 0331.35002

[20] Ekeland I., Temam R., Convex Analysis and Variational Problems, Stud. Math. Appl., vol. 1, North-Holland, Amsterdam, 1976. | MR 463994 | Zbl 0322.90046

[21] Evans L.C., Gariepy R.F., Measure Theory and Fine Properties of Functions, Stud. Adv. Math., vol. 5, CRC Press, Boca Raton, FL, 1992. | MR 1158660 | Zbl 0804.28001

[22] Giaquinta M., Modica G., Souček J., Functionals with linear growth in the calculus of variations, Comment. Math. Univ. Carolin. 20 (1979) 143-156. | MR 526154 | Zbl 0409.49006

[23] Goffman C., Serrin J., Sublinear functions of measures and variational integrals, Duke Math. J. 31 (1964) 159-178. | MR 162902 | Zbl 0123.09804

[24] Hüsseinov F., Relaxation of multidimensional variational problems with constraints of general form, Nonlinear Anal. 45 (2001) 651-659. | MR 1838952 | Zbl 1001.49022

[25] Ishii H., Loreti P., Relaxation in an L ∞ -optimization problem, Proc. Roy. Soc. Edinburgh Sect. A 133 (2003) 599-615. | MR 1983688 | Zbl 1042.49013

[26] Ishii H., Loreti P., Relaxation of Hamilton-Jacobi equations, Arch. Rational Mech. Anal. 169 (2003) 265-304. | Zbl 1036.70011

[27] Kawohl B., On a family of torsional creep problems, J. Reine Angew. Math. 410 (1990) 1-22. | MR 1068797 | Zbl 0701.35015

[28] Kinderlehrer D., Stampacchia G., An Introduction to Variational Inequalities and Their Applications, Pure Appl. Math., vol. 88, Academic Press, New York, 1980. | MR 567696 | Zbl 0457.35001

[29] Lions P.-L., Generalized Solutions of Hamilton-Jacobi Equations, Pitman Res. Notes Math. Ser., vol. 69, Longman Scientific & Technical, Harlow, 1982. | Zbl 0497.35001

[30] Marcellini P., Sbordone C., Semicontinuity problems in the calculus of variations, Nonlinear Anal. 4 (1980) 241-257. | MR 563807 | Zbl 0537.49002

[31] Morrey C.B., Multiple Integrals in the Calculus of Variations, Grundlehren Math. Wiss., vol. 130, Springer, Berlin, 1966. | MR 202511 | Zbl 0142.38701

[32] Rockafellar R.T., Convex Analysis, Princeton Math. Ser., vol. 28, Princeton University Press, Princeton, 1972. | Zbl 0193.18401

[33] Rockafellar R.T., Wets R.J.-B., Variational Analysis, Grundlehren Math. Wiss., vol. 317, Springer, Berlin, 1998. | MR 1491362 | Zbl 0888.49001

[34] Ting T.W., Elastic-plastic torsion of simply connected cylindrical bars, Indiana Univ. Math. J. 20 (1971) 1047-1076. | MR 277161 | Zbl 0205.56203

[35] Treloar L.R.G., The Physics of Rubber Elasticity, Clarendon Press, Oxford, 1975.

[36] Ziemer W.P., Weakly Differentiable Functions, Grad. Texts in Math., vol. 120, Springer, Berlin, 1989. | MR 1014685 | Zbl 0692.46022