Homogénéisation

Hedy Attouch

Séminaire Bourbaki (1987-1988)

  • Volume: 30, page 7-30
  • ISSN: 0303-1179

How to cite

top

Attouch, Hedy. "Homogénéisation." Séminaire Bourbaki 30 (1987-1988): 7-30. <http://eudml.org/doc/110103>.

@article{Attouch1987-1988,
author = {Attouch, Hedy},
journal = {Séminaire Bourbaki},
keywords = {energetic methods; incomplete information; stochastic homogenization; rapidly oscillating coefficients; compensated compactness; Gamma- convergence; epi-convergence; Mosco-convergence},
language = {fre},
pages = {7-30},
publisher = {Société Mathématique de France},
title = {Homogénéisation},
url = {http://eudml.org/doc/110103},
volume = {30},
year = {1987-1988},
}

TY - JOUR
AU - Attouch, Hedy
TI - Homogénéisation
JO - Séminaire Bourbaki
PY - 1987-1988
PB - Société Mathématique de France
VL - 30
SP - 7
EP - 30
LA - fre
KW - energetic methods; incomplete information; stochastic homogenization; rapidly oscillating coefficients; compensated compactness; Gamma- convergence; epi-convergence; Mosco-convergence
UR - http://eudml.org/doc/110103
ER -

References

top
  1. [1 ] H. Attouch - Variational convergence for functions and operators. ApplicableMathematics Series, Pitman (1984). Zbl0561.49012MR773850
  2. [2 ] H. Attouch - Introduction à l'homogénéisation d'inéquations variationnelles, Rend.Sem.Mat.Univers.Politecn. Torino (Italy)40, 2, (1981). Zbl0523.35004MR724197
  3. [3 ] H. Attouch, D. Aze et R. Wets - Convergence of convex-concave saddle functions. Continuity properties of the Legendre-Fenchel transform with applications to convex programming and mechanics, to appear Annales de l'Institut H. Poincaré. Zbl0667.49009
  4. [ 4 ] H. Attouch et G. Buttazzo - Homogénization of reinforced periodic one-codimensional structures, publication AVAMAC,Université de Perpignan 86-06 (1986). A paraître Ann.Scuola Normale Pisa. Zbl0654.73017MR951229
  5. [5 ] H. Attouch et F. Murat - Homogenization of fissured elastic materials, Publication AVAMAC, Université de Perpignan 85-03, (1985), Vol.1. 
  6. [ 6 ] H. Attouch et C. Picard - Variational inequalities with varying obstacles, Journal of functional analysis, Vol.50, n°3 (1983). MR695419
  7. [7 ] H. Attouch et R. Wets - Approximation and convergence in nonlinear optimization; Nonlinear programning 4.Ed by Mangasarian, Meyer, Robinson. Academic Press (1981), 367-394. MR663386
  8. [8 ] N.S. Bahvalov et G. Panasenko - Averaged processes in periodic media, Moscow, Nauka, (1984) (in russian). 
  9. [ 9 ] A. Bensoussan, J.L. Lions et G. Papanicolaou - Asymptotic analysis for periodic structures, North Holland (1978). Zbl0404.35001MR503330
  10. [10] L. Boccardo et F. Murat - Homogénéisation de problèmes quasi-linéaires, (Bressanone,7-9 sett.1981).Pitagora Editrice,Bologna,(1982),pp.13-51. 
  11. [11 ] G. Bouchitte - Convergence et Relaxation de fonctionnelles du calcul des variations à croissance linéaire. Application à l'homogénéisation en plasticité, Ch.5 thèse d'état, Université de Perpignan (1987). A paraître Ann. Fac. Sc. Toulouse. Zbl0663.49002
  12. [12 ] B. Buttazzo et G. Dal Maso - Γ-limits of integral functionals, J. Analyse Math.,37, (1980), 145-185. Zbl0446.49012
  13. [ 13 ] L. Carbone - Sur un problème d'homogénéisation avec des contraintes sur le gradient, J. Math.Pures.Appl.58, 275-297 (1979). Zbl0387.49028MR544254
  14. [14 ] L. Carbone et C. Sbordone - Some properties of Γ-limits of integral functionals, Ann. Mat.Pura Appl (4) 122, 1-60 (1979). Zbl0474.49016
  15. [15] D. Cioranescu et F. Murat - Un terme étrange venu d'ailleurs, I & 2. Nonlinear partial differential and their applications, Collège de France Seminar, Vol II & III, ed. H.Brezis & J.L.Lions. Research Notes in Math. Nos 60 & 70, Pitman, 98-138, 154-178 (1982). Zbl0496.35030
  16. [16] D. Cioranescu et J. Saint Jean Paulin - Homogenization in open sets with holes, J.Math.Pures Appl.71, 590-607 (1979). Zbl0427.35073MR548785
  17. [17] D. Cioranescu et J. Saint Jean Paulin - Reinforced and alveolar structures, publication 85042 du Laboratoire d'Analyse Numérique Paris VI, (1985). 
  18. [18] G. Dal Maso et L. Modica - A general theory of variational functionals. "Topics in Functional Analysis 1980-81", Scuola Normale Superiore, Pisa (1982), 149-221. Zbl0493.49005MR671757
  19. [19] G. Dal Maso et L. Modica - Stochastic homogenization and ergodic theory, proceedings Erice 1984, ed.R.Conti, E.De Giorgi, F.Gianessi, Ch.15. Lectures Notes Springer. 
  20. [20 ] E. De Giorgi - Convergence problems for functionals and operators, proceedings Rome 1978, ed by E.De Giorgi, E.Magenès, U.Mosco, Pitagora, Bologna (1979), 131-188. Zbl0405.49001MR533166
  21. [ 21 ] E. De Giorgi - G-operators and Γ-convergence, proceedings International Congress of Mathematicians, Warzawa1983. Zbl0568.35025
  22. [22 ] G. Duvaut - Comportement macroscopique d'une plaque perforée périodiquement, Lectures Notes in Mathematics, n°594, Springer-Verlag, (1977), 131-145. Zbl0363.35001MR462086
  23. [23 ] J.L. Joly - Une famille de topologies sur l'ensemble des fonctions convexes pour lesquelles la polarité est bicontinue, J. Math.Pures Appl., 52, 421- 441 (1973). Zbl0282.46005MR500129
  24. [24 ] R. Kohn et G. Strang - Structural design and optimization, homogenization and relaxation of variational problems, in Macroscopic Properties of Disordered Media, Burridge, Childress, Papanicolaou ed., Lectures Notes in Physics154, Springer (1982), 131-147. Zbl0539.73103
  25. [25 ] C. Licht - Frottement, viscoplasticité et homogeneisationThèseUniversité Montpellier (1987). 
  26. [ 26 ] J.L. Lions - Some methods in Mathematical Analysis and their Control, Science Press, Beijing (China) - Gordon BreachNew York (1984) Zbl0542.93034
  27. [ 27 ] K.A. Lurie et A.V. Cherkaev - Optimal structural design and relaxed controls, Opt.Control.Appl.Math.4 (1983) 387-392. Zbl0526.49003
  28. [28] P. Marcellini - Periodic solutions and homogenization of nonlinear variational problems, Ann.Mat.Pura Appl.117 (1978), 139-152. Zbl0395.49007MR515958
  29. [ 29 ] A.V. Marchenko et E.Ya. Hruslov - Boundary value problems in domains with close-grained boundaries (Russian), Naukova Dumka, Kiev (1974). Zbl0289.35002
  30. [30] U. Mosco - Convergence of convex sets and of solutions of variational inequalities, Advances in Math., 3, (1699), 510-585). Zbl0192.49101MR298508
  31. [31] F. Murat - Compacité par compensation, Ann.Sc.Nonn.Sup.Pisa, Cl.Sci (4) 5 (1978) 481-507. Zbl0399.46022MR506997
  32. [32 ] F. Murat - Compacité par compensation II, Proc.Int.Meeting on "Recent Methods in nonlinear analysis", Rome1978, ed.E.De Giorgi, E.Magenes, U.Mosco, Pitagora ed.Bologna, 245-256 (1979). Zbl0427.35008MR533170
  33. [33] F. Murat - Compacité par compensation : condition nécessaire et suffisante de continuité faible sous une hypothèse de rang constant, Ann.Sc.Norm. Sup.Pisa.Cl.Sci. (4) 8, 69-102 (1981). Zbl0464.46034MR616901
  34. [34 ] F. Murat - H-convergence. Rapport du séminaire d'analyse fonctionnelle et numérique del'Université d'Alger (1978). 
  35. [35 ] F. Murat et L. Tartar - Optimality conditions and homogenization in Nonlinear Variational Problems, ed. by A.Marino et al., Research Notes in Maths, 127, Pitman, London (1985), pp.1-8. Zbl0569.49015MR807532
  36. [36] G.C. Papanicolaou et S.R.S. Varadhan - Boundary value problems with rapidly oscillating random coefficients, Proceed.of Colloq.on Random fields rigorous results in statistical mechanics and quantum fields, ed by J.Fritz, J.L.Lebowitz, D.Szasz. Colloque Mathematics Soviet. Janos Bolyai, 10, North Holland, Amsterdam (1979), 835-873. Zbl0499.60059MR712714
  37. [37] G. Salinetti et R. Wets - On the convergence of closed - valued measurable multifunctions, Trans.Amer.Maths.Soc.,266, 275-289 (1981). Zbl0501.28005MR613796
  38. [38] E. Sanchez-Palencia - Nonhomogenous media and vibration theory, Lecture Notes in Physics, Springer, 127 (1980). Zbl0432.70002MR578345
  39. [39] C. Sbordone - Su alcune applicazioni di un tipo di convergenza variazionale, Ann.Sc.Norm.Sup.Pisa.Cl.Sci.(4), 2, (1975), 617-638. Zbl0317.49012MR417753
  40. [40] S. Spagnolo - Sulla convergenza delle soluzioni di equazioni paraboliche ed ellitiche, Ann.Sc.Norm.Sup.Pisa.Cl.Sci.Fis.Mat.(3),22, (1968), 575-597. Zbl0174.42101MR240443
  41. [41] P. Suquet - Plasticité et homogénéisation, Thèse, Univ. Paris XI (1982). 
  42. [42 ] L. Tartar - Cours Peccot, Collège de France, Paris (1977). 
  43. [43 ] L. Tartar - Compensated compactness and applications to partial differential equations. Nonlinear analysis and mechanics, Heriot-Watt sy mposium vol. IV. Research Notes in Mathematics39. Pitman (1979) 136-212. Zbl0437.35004MR584398
  44. [44 ] L. Tartar - Problèmes de contrôle de coefficients dans des équations aux dérivées partielles, in control theory, numerical methods and computer systems modelling, Lecture notes in economical and mathematical systems107, Springer (1974), 420-426. Zbl0318.49010MR428166
  45. [45] L. Tartar - Estimations fines de coefficients homogénéisés, Ennio De Giorgi colloquium ed by P.Krée, Research Notes in Mathematics125, Pitman, London (1985). Zbl0586.35004MR909716
  46. [46] V.V. Yurinskij - Averaging an elliptic value problem with random coefficients, Siberian Math.Journal, 21 (1980) 470-482. Zbl0453.35090
  47. [47 ] R. Wets - Convergence of convex functions, variational inequalities and convex optimization problems, in variational inequalities and complementary problems, eds.P.Cottle, F.Gianessi, J.L.Lions, Wiley, Chichester (UK) (1980), 375-403. Zbl0481.90066MR578760

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.