@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}, publisher = {Elsevier}, volume = {24}, number = {1}, year = {2007}, doi = {10.1016/j.anihpc.2005.12.003}, mrnumber = {2286561}, zbl = {1112.49014}, language = {en}, url = {http://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 - http://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 http://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. http://www.numdam.org/articles/10.1016/j.anihpc.2005.12.003/
[1] Variational Convergence for Functions and Operators, Pitman, London, 1984. | MR | Zbl
,[2] Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations, Pitman Res. Notes Math. Ser., vol. 207, Longman Scientific & Technical, Harlow, 1989. | MR | Zbl
,[3] 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 | Zbl
, , , ,[4] Homogenization of Neumann problems for unbounded functionals, Boll. Un. Mat. Ital. Sez. B Artic. Ric. Mat. 2-B (8) (1999) 463-491. | MR | Zbl
, , ,[5] On the relaxation of some classes of unbounded integral functionals, Matematiche 51 (1996) 221-256, (special issue in Honour of Francesco Guglielmino). | MR | Zbl
, ,[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). | MR | Zbl
, ,[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. | MR | Zbl
, ,[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. | MR | Zbl
, ,[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. | MR | Zbl
, ,[11] Direct Methods in the Calculus of Variations, Appl. Math. Sci., vol. 78, Springer, Berlin, 1989. | MR | Zbl
,[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. | MR | Zbl
, ,[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. | MR | Zbl
, , ,[16] On the relaxation of some classes of Dirichlet minimum problems, Comm. Partial Differential Equations 24 (1999) 975-1006. | MR | Zbl
, ,[17] On the relaxation of variational integrals with pointwise continuous-type gradient constraints, Appl. Math. Optim. 51 (2005) 251-277. | MR | Zbl
, ,[18] Homogenization of Dirichlet problems for some types of integral functionals, Ricerche Mat. 46 (1997) 177-202. | MR | Zbl
, ,[19] Inequalities in Mechanics and Physics, Grundlehren Math. Wiss., vol. 219, Springer, Berlin, 1976. | MR | Zbl
, ,[20] Convex Analysis and Variational Problems, Stud. Math. Appl., vol. 1, North-Holland, Amsterdam, 1976. | MR | Zbl
, ,[21] Measure Theory and Fine Properties of Functions, Stud. Adv. Math., vol. 5, CRC Press, Boca Raton, FL, 1992. | MR | Zbl
, ,[22] Functionals with linear growth in the calculus of variations, Comment. Math. Univ. Carolin. 20 (1979) 143-156. | MR | Zbl
, , ,[23] Sublinear functions of measures and variational integrals, Duke Math. J. 31 (1964) 159-178. | MR | Zbl
, ,[24] Relaxation of multidimensional variational problems with constraints of general form, Nonlinear Anal. 45 (2001) 651-659. | MR | Zbl
,[25] Relaxation in an -optimization problem, Proc. Roy. Soc. Edinburgh Sect. A 133 (2003) 599-615. | MR | Zbl
, ,[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. | MR | Zbl
,[28] An Introduction to Variational Inequalities and Their Applications, Pure Appl. Math., vol. 88, Academic Press, New York, 1980. | MR | Zbl
, ,[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. | MR | Zbl
, ,[31] Multiple Integrals in the Calculus of Variations, Grundlehren Math. Wiss., vol. 130, Springer, Berlin, 1966. | MR | Zbl
,[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. | MR | Zbl
, ,[34] Elastic-plastic torsion of simply connected cylindrical bars, Indiana Univ. Math. J. 20 (1971) 1047-1076. | MR | Zbl
,[35] The Physics of Rubber Elasticity, Clarendon Press, Oxford, 1975.
,[36] Weakly Differentiable Functions, Grad. Texts in Math., vol. 120, Springer, Berlin, 1989. | MR | Zbl
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