EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 7 (2002) ESAIM: COCV, 7 (2002) 379-406 References
Free Access
Issue
ESAIM: COCV
Volume 7, 2002
Page(s) 379 - 406
DOI https://doi.org/10.1051/cocv:2002060
Published online 15 September 2002
  1. G. Alessandrini and R. Magnanini, Elliptic equation in divergence form, geometric critical points of solutions and Stekloff eigenfunctions. SIAM J. Math. Anal. 25 (1994) 1259-1268. [CrossRef] [MathSciNet] [Google Scholar]
  2. G. Alessandrini and V. Nesi, Univalent σ-harmonic mappings. Arch. Rational Mech. Anal. 158 (2001) 155-171. [Google Scholar]
  3. G. Alessandrini and V. Nesi, Univalent σ-harmonic mappings: Connections with quasiconformal mappings, Quaderni Matematici II serie, 510 Novembre 2001. Dipartimento di Scienze Matematiche, Trieste. J. Anal. Math. (to appear). [Google Scholar]
  4. G. Allaire and G. Francfort, Existence of minimizers for non-quasiconvex functionals arising in optimal design. Ann. Inst. H. Poincaré Anal. Non Linéaire 15 (1998) 301-339. [CrossRef] [MathSciNet] [Google Scholar]
  5. G. Allaire and V. Lods, Minimizers for a double-well problem with affine boundary conditions. Proc. Roy. Soc. Edinburgh Sect. A 129 (1999) 439-466. [MathSciNet] [Google Scholar]
  6. K. Astala, Area distortion of quasiconformal mappings. Acta Math. 173 (1994) 37-60. [CrossRef] [MathSciNet] [Google Scholar]
  7. K. Astala and M. Miettinen, On quasiconformal mappings and 2-dimensional G-closure problems. Arch. Rational Mech. Anal. 143 (1998) 207-240. [CrossRef] [MathSciNet] [Google Scholar]
  8. K. Astala and V. Nesi, Composites and quasiconformal mappings: New optimal bounds. University of Jyväskylä, Department of Mathematics, Preprint 233, Ottobre 2000, Jyväskylä, Finland. Calc. Var. Partial Differential Equations (to appear). [Google Scholar]
  9. J.M. Ball and R.D. James, Fine phase mixtures as minimizers of energy. Arch. Rational Mech. Anal. 100 (1987) 13-52. [Google Scholar]
  10. P. Bauman, A. Marini and V. Nesi, Univalent solutions of an elliptic system of partial differential equations arising in homogenization. Indiana Univ. Math. J. 50 (2001). [Google Scholar]
  11. A. Bensoussan, J.-L. Lions and G. Papanicolaou, Asymptotic analysis for periodic structures. North Holland, Amsterdam (1978). [Google Scholar]
  12. L. Bers, F. John and M. Schechter, Partial Differential Equations. Interscience, New York (1964). [Google Scholar]
  13. L. Bers and L. Nirenberg, On a representation theorem for linear elliptic systems with discontinuous coefficients and its applications, in Convegno Internazionale sulle Equazioni alle Derivate Parziali. Cremonese, Roma (1955) 111-138. [Google Scholar]
  14. A. Cherkaev, Necessary conditions technique in optimization of structures. J. Mech. Phys. Solids (accepted). [Google Scholar]
  15. A. Cherkaev, Variational methods for structural optimization. Springer-Verlag, Berlin, Appl. Math. Sci. 140 (2000). [Google Scholar]
  16. A. Cherkaev and L.V. Gibiansky, Extremal structures of multiphase heat conducting composites. Int. J. Solids Struct. 18 (1996) 2609-2618. [CrossRef] [Google Scholar]
  17. A.M. Dykhne, Conductivity of a two dimensional two-phase system. Soviet Phys. JETP 32 (1971) 63-65. [Google Scholar]
  18. A. Eremenko and D.H. Hamilton, The area distortion by quasiconformal mappings. Proc. Amer. Math. Soc. 123 (1995) 2793-2797. [MathSciNet] [Google Scholar]
  19. G. Francfort and G.W. Milton, Optimal bounds for conduction in two-dimensional, multiphase polycrystalline media. J. Stat. Phys. 46 (1987) 161-177. [CrossRef] [Google Scholar]
  20. G. Francfort and F. Murat, Optimal bounds for conduction in two-dimensional, two phase, anisotropic media, in Non-classical continuum mechanics, edited by R.J. Knops and A.A. Lacey. Cambridge, London Math. Soc. Lecture Note Ser. 122 (1987) 197-212. [Google Scholar]
  21. L.V. Gibiansky and O. Sigmund, Multiphase composites with extremal bulk modulus. J. Mech. Phys. Solids 48 (2000) 461-498. [CrossRef] [MathSciNet] [Google Scholar]
  22. Y. Grabovsky, The G-closure of two well ordered anisotropic conductors. Proc. Roy. Soc. Edinburgh Sect. A 123 (1993) 423-432. [MathSciNet] [Google Scholar]
  23. Z. Hashin and S. Shtrikman, A variational approach to the theory of effective magnetic permeability of multiphase materials. J. Appl. Phys. 33 (1962) 3125-3131. [CrossRef] [Google Scholar]
  24. J. Keller, A theorem on the conductivity of a composite medium. J. Math. Phys. 5 (1964) 548-549. [CrossRef] [Google Scholar]
  25. W. Kohler and G. Papanicolaou, Bounds for the effective conductivity of random media. Springer, Lecture Notes in Phys. 154, p. 111. [Google Scholar]
  26. R.V. Kohn, The relaxation of a double energy. Continuum Mech. Thermodyn. 3 (1991) 193-236. [CrossRef] [MathSciNet] [Google Scholar]
  27. R.V. Kohn and G.W. Milton, On bounding the effective conductivity of anisotropic composites, in Homogenization and effective moduli of materials and media, edited by J.L. Ericksen, D. Kinderlehrer, R. Kohn and J.-L. Lions. Springer, New York (1986) 97-125. [Google Scholar]
  28. R.V. Kohn and G. Strang, Optimal design and relaxation of variational problems I, II, III. Comm. Pure Appl. Math. 39 (1986) 113-137, 139-182, 353-377. [Google Scholar]
  29. O. Lehto and K.I. Virtanen, Quasiconformal Mappings in the Plane. Springer, Berlin (1973). [Google Scholar]
  30. K.A. Lurie and A.V. Cherkaev, Exact estimates of conductivity of composites formed by two isotropically conducting media taken in prescribed proportions. Proc. Roy. Soc. Edinburgh Sect. A 99 (1984) 71-87. [MathSciNet] [Google Scholar]
  31. K.A. Lurie and A.V. Cherkaev, G-closure of a set of anisotropically conducting media in the two-dimensional case. J. Optim. Theory Appl. 42 (1984) 283-304. [CrossRef] [MathSciNet] [Google Scholar]
  32. K.A. Lurie and A.V. Cherkaev, The problem of formation of an optimal isotropic multicomponent composite. J. Optim. Theory Appl. 46 (1985) 571-589. [CrossRef] [MathSciNet] [Google Scholar]
  33. K.S. Mendelson, Effective conductivity of a two-phase material with cylindrical phase boundaries. J. Appl. Phys. 46 (1975) 917. [CrossRef] [Google Scholar]
  34. G.W. Milton, Concerning bounds on the transport and mechanical properties of multicomponent composite materials. Appl. Phys. A 26 (1981) 125-130. [CrossRef] [Google Scholar]
  35. G.W. Milton, On characterizing the set of possible effective tensors of composites: The variational method and the translation method. Comm. Pure Appl. Math. 43 (1990) 63-125. [CrossRef] [MathSciNet] [Google Scholar]
  36. G.W. Milton and R.V. Kohn, Variational bounds on the effective moduli of anisotropic composites. J. Mech. Phys. Solids 36 (1988) 597-629. [CrossRef] [MathSciNet] [Google Scholar]
  37. G.W. Milton and V. Nesi, Optimal G-closure bounds via stability under lamination. Arch. Rational Mech. Anal. 150 (1999) 191-207. [CrossRef] [Google Scholar]
  38. S. Müller, Variational models for microstructure and phase transitions, Calculus of variations and geometric evolution problems. Cetraro (1996) 85-210. Springer, Berlin, Lecture Notes in Math. 1713 (1999). [Google Scholar]
  39. F. Murat, Compacité par compensation : condition nécessaire et suffisante de continuité faible sous une hypothèse de rang constant. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 8 (1981) 69-102. [MathSciNet] [Google Scholar]
  40. F. Murat and L. Tartar, Calcul des variations et homogénéisation, in Les Méthodes de L'Homogénéisation : Théorie et Applications en Physique. Eyrolles (1985) 319-369. [Google Scholar]
  41. V. Nesi, Using quasiconvex functionals to bound the effective conductivity of composite materials. Proc. Roy. Soc. Edinburgh Sect. A 123 (1993) 633-679. [MathSciNet] [Google Scholar]
  42. V. Nesi, Bounds on the effective conductivity of 2 d composites made of n ≥ 3 isotropic phases in prescribed volume fractions: The weighted translation method. Proc. Roy. Soc. Edinburgh Sect. A 125 (1995) 1219-1239. [CrossRef] [MathSciNet] [Google Scholar]
  43. V. Nesi, Quasiconformal mappings as a tool to study the effective conductivity of two dimensional composites made of n ≥ 2 anisotropic phases in prescribed volume fraction. Arch. Rational Mech. Anal. 134 (1996) 17-51. [CrossRef] [MathSciNet] [Google Scholar]
  44. K. Schulgasser, Sphere assemblage model for polycrystal and symmetric materials. J. Appl. Phys. 54 (1982) 1380-1382. [CrossRef] [Google Scholar]
  45. K. Schulgasser, A reciprocal theorem in two dimensional heat transfer and its implications. Internat. Commun. Heat Mass Transfer 19 (1992) 497-515. [Google Scholar]
  46. S. Spagnolo, Sul limite delle soluzioni di problemi di Cauchy relativi all'equazione del calore. Ann. Scuola Norm. Sup. Pisa (3) 21 (1967) 657-699. [MathSciNet] [Google Scholar]
  47. S. Spagnolo, Sulla convergenza di soluzioni di equazioni paraboliche ed ellittiche. Ann. Scuola Norm. Sup. Pisa (3) 22 (1968) 571-597. [Google Scholar]
  48. L. Tartar, Estimations de coefficients homogénéisés. Springer, Berlin, Lecture Notes in Math. 704 (1978) 364-373. English translation: Estimations of homogenized coefficients, in Topics in the mathematical modelling of composite materials, 9-20. Birkhäuser, Progr. Nonlinear Differential Equations Appl. 31. [Google Scholar]
  49. L. Tartar, Estimations fines des coefficients homogénéisés, in Ennio De Giorgi's Colloquium (Paris 1983), edited by P. Kree. Pitman, Boston (1985) 168-187. [Google Scholar]
  50. L. Tartar, Compensated compactness and applications to p.d.e. in nonlinear analysis and mechanics, in Heriot-Watt Symposium, Vol. IV, edited by R.J. Knops. Pitman, Boston (1979) 136-212. [Google Scholar]
  51. L. Tonelli, Fondamenti di calcolo delle variazioni. Zanichelli, Bologna (1921). [Google Scholar]
  52. I.N. Vekua, Generalized Analytic Functions. Pergamon, Oxford (1962). [Google Scholar]
  53. V.V. Zhikov, Estimates for the averaged matrix and the averaged tensor. Russian Math. Surveys (46) 3 (1991) 65-136. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.