On integral representation, relaxation and homogenization for unbounded functionals

Luciano Carbone; Riccardo De Arcangelis

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1997)

  • Volume: 8, Issue: 2, page 129-135
  • ISSN: 1120-6330

Abstract

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A theory of integral representation, relaxation and homogenization for some types of variational functionals taking extended real values and possibly being not finite also on large classes of regular functions is presented. Some applications to gradient constrained relaxation and homogenization problems are given.

How to cite

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Carbone, Luciano, and De Arcangelis, Riccardo. "On integral representation, relaxation and homogenization for unbounded functionals." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 8.2 (1997): 129-135. <http://eudml.org/doc/244328>.

@article{Carbone1997,
abstract = {A theory of integral representation, relaxation and homogenization for some types of variational functionals taking extended real values and possibly being not finite also on large classes of regular functions is presented. Some applications to gradient constrained relaxation and homogenization problems are given.},
author = {Carbone, Luciano, De Arcangelis, Riccardo},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Integral representation; Relaxation; Homogenization; integral representation; relaxation; homogenization; variational functionals},
language = {eng},
month = {7},
number = {2},
pages = {129-135},
publisher = {Accademia Nazionale dei Lincei},
title = {On integral representation, relaxation and homogenization for unbounded functionals},
url = {http://eudml.org/doc/244328},
volume = {8},
year = {1997},
}

TY - JOUR
AU - Carbone, Luciano
AU - De Arcangelis, Riccardo
TI - On integral representation, relaxation and homogenization for unbounded functionals
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1997/7//
PB - Accademia Nazionale dei Lincei
VL - 8
IS - 2
SP - 129
EP - 135
AB - A theory of integral representation, relaxation and homogenization for some types of variational functionals taking extended real values and possibly being not finite also on large classes of regular functions is presented. Some applications to gradient constrained relaxation and homogenization problems are given.
LA - eng
KW - Integral representation; Relaxation; Homogenization; integral representation; relaxation; homogenization; variational functionals
UR - http://eudml.org/doc/244328
ER -

References

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  1. AMBROSIO, L. - DAL MASO, G., On the relaxation in B V Ω ; R n , of quasi-convex integrals. J. Funct. Anal., 109, 1992, 76-97. Zbl0769.49009MR1183605DOI10.1016/0022-1236(92)90012-8
  2. BENSOUSSAN, A. - LIONS, J. L. - PAPANICOLAOU, G., Asymptotic Analysis for Periodic Structures. Studies in Mathematics and its Applications, 5, North-Holland, Amsterdam1978. Zbl0404.35001MR503330
  3. BOUCHITTÉ, G. - DAL MASO, G., Integral representation and relaxation of convex local functional on B V Ω . Ann. Sc. Norm. Sup. Pisa, 20, 1993, 483-533. Zbl0802.49008MR1267597
  4. BREZIS, H. - SIBONY, M., Equivalence de deux inéquations variationnelles et applications. Arch. Rational Mech. Anal., 41, 1971, 254-265. Zbl0214.11104MR346345
  5. BUTTAZZO, G., Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations. Pitman Research Notes in Mathematics Series, 207, Longman Scientific & Technical, Harlow1989. Zbl0669.49005MR1020296
  6. CARBONE, L. - SALERNO, S., Further results on a problem of homogenization with constraints on the gradient. J. Analyse Math., 44, 1984-85, 1-20. Zbl0574.35006MR801284DOI10.1007/BF02790187
  7. CORBO ESPOSITO, A. - DE ARCANGELIS, R., Homogenization of Dirichlet problems with nonnegative bounded constraints on the gradient. J. Analyse Math., 64, 1994, 53-96. Zbl0822.49012MR1303508DOI10.1007/BF03008405
  8. CORBO ESPOSITO, A. - DE ARCANGELIS, R., A characterization of families of function sets described by constraints on the gradient. Ann. Inst. Henri Poincaré - Analyse non linéaire, 11, 1994, 553-609. Zbl0839.49007MR1302280
  9. DAL MASO, G., An introduction to Γ -convergence. Progress in Nonlinear Differential Equations and Their Applications, 8, Birkhäuser, Boston-Basel-Berlin1993. Zbl0816.49001MR1201152DOI10.1007/978-1-4612-0327-8
  10. DE GIORGI, E. - FRANZONI, T., Su un tipo di convergenza variazionale. Atti Acc. Lincei Rend, fis., s. 8, 58, 1975, 842-850. Zbl0339.49005MR448194
  11. DE GIORGI, E. - LETTA, G., Une notion générale de convergence faible pour des fonctions croissantes d'ensemble. Ann. Sc. Norm. Sup. Pisa, 4, 1977, 61-99. Zbl0405.28008MR466479
  12. DUVAUT, G. - LIONS, J. L., Inequalities in Mechanics and Physics. Grundlehren der mathematischen Wissenschaften, 219, Springer-Verlag, Berlin-Heidelberg-New York1976. Zbl0331.35002MR521262
  13. EKELAND, I. - TEMAM, R., Convex Analysis and Variational Problems. Studies in Mathematics and its Applications, 1, North-Holland, Amsterdam1976. Zbl0322.90046MR463994
  14. GLOWINSKI, R. - LANCHON, H., Torsion élastoplastique d'une barre cylindrique de section multiconnexe. J. Mécanique, 12, 1973, 151-171. Zbl0273.73023MR363114
  15. GOFFMAN, C. - SERRIN, J., Sublinear functions of measures and variational integrals. Duke Math. J., 31, 1964, 159-178. Zbl0123.09804MR162902
  16. RAUCH, J. - TAYLOR, M., Electrostatic screening. J. Math. Phys., 16, 1975, 284-288. MR382834

Citations in EuDML Documents

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  1. Luciano Carbone, Doina Cioranescu, Riccardo De Arcangelis, Antonio Gaudiello, Homogenization of unbounded functionals and nonlinear elastomers. The case of the fixed constraints set
  2. Luciano Carbone, Antonio Corbo Esposito, Riccardo De Arcangelis, Homogenization of Neumann problems for unbounded integral functionals
  3. Luciano Carbone, Doina Cioranescu, Riccardo De Arcangelis, Antonio Gaudiello, Homogenization of unbounded functionals and nonlinear elastomers. The case of the fixed constraints set

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