Free Access
Issue
ESAIM: COCV
Volume 15, Number 2, April-June 2009
Page(s) 322 - 366
DOI https://doi.org/10.1051/cocv:2008039
Published online 24 June 2008
  1. L. Ambrosio, A. Coscia and G. Dal Maso, Fine properties of functions with bounded deformation. Arch. Rational Mech. Anal. 139 (1997) 201–238. [Google Scholar]
  2. L. Ambrosio, N. Fusco and D. Pallara, Functions of bounded variation and free discontinuity problems, Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York (2000). [Google Scholar]
  3. J.M. Ball and R.D. James, Fine phase mixtures as minimisers of energy. Arch. Rational Mech. Anal. 100 (1987) 13–52. [Google Scholar]
  4. J.M. Ball and R.D. James, Proposed experimental tests of a theory of fine microstructure and the two well problem. Phil. Trans. Roy. Soc. London Ser. A 338 (1992) 389–450. [Google Scholar]
  5. M. Chipot, The appearance of microstructures in problems with incompatible wells and their numerical approach. Numer. Math. 83 (1999) 325–352. [CrossRef] [MathSciNet] [Google Scholar]
  6. M. Chipot and D. Kinderlehrer, Equilibrium configurations of crystals. Arch. Rational Mech. Anal. 103 (1988) 237–277. [MathSciNet] [Google Scholar]
  7. M. Chipot and S. Müller, Sharp energy estimates for finite element approximations of non-convex problems, in Variations of domain and free-boundary problems in solid mechanics (Paris, 1997), Solid Mech. Appl. 66, Kluwer Acad. Publ., Dordrecht (1999) 317–325. [Google Scholar]
  8. S. Conti, Branched microstructures: scaling and asymptotic self-similarity. Comm. Pure Appl. Math. 53 (2000) 1448–1474. [CrossRef] [MathSciNet] [Google Scholar]
  9. S. Conti and B. Schweizer, Rigidity and Gamma convergence for solid-solid phase transitions with Formula -invariance. Comm. Pure Appl. Math. 59 (2006) 830–868. [CrossRef] [MathSciNet] [Google Scholar]
  10. S. Conti, D. Faraco and F. Maggi, A new approach to counterexamples to Formula estimates: Korn's inequality, geometric rigidity, and regularity for gradients of separately convex functions. Arch. Rational Mech. Anal. 175 (2005) 287–300. [Google Scholar]
  11. S. Conti, G. Dolzmann and B. Kirchheim, Existence of Lipschitz minimizers for the three-well problem in solid-solid phase transitions. Ann. Inst. H. Poincaré Anal. Non Linéaire 24 (2007) 953–962. [CrossRef] [MathSciNet] [Google Scholar]
  12. B. Dacorogna and P. Marcellini, General existence theorems for Hamilton-Jacobi equations in the scalar and vectorial cases. Acta Math. 178 (1997) 1–37. [CrossRef] [MathSciNet] [Google Scholar]
  13. C. De Lellis and L. Székelyhidi, The Euler equations as a differential inclusion. Ann. Math. (to appear). [Google Scholar]
  14. G. Dolzmann and K. Bhattacharya, Relaxed constitutive relations for phase transforming materials. The J. R. Willis 60th anniversary volume. J. Mech. Phys. Solids 48 (2000) 1493–1517. [CrossRef] [MathSciNet] [Google Scholar]
  15. G. Dolzmann and B. Kirchheim, Liquid-like behavior of shape memory alloys. C. R. Math. Acad. Sci. Paris 336 (2003) 441–446. [CrossRef] [MathSciNet] [Google Scholar]
  16. G. Dolzmann and S. Müller, Microstructures with finite surface energy: the two-well problem. Arch. Rational Mech. Anal. 132 (1995) 101–141. [Google Scholar]
  17. L.C. Evans and R.F. Gariepy, Measure theory and fine properties of functions, Studies in Advanced Mathematics. CRC Press, Boca Raton, FL (1992). [Google Scholar]
  18. G. Friesecke, R.D. James and S. Müller, A theorem on geometric rigidity and the derivation of nonlinear plate theory from three dimensional elasticity. Comm. Pure Appl. Math. 55 (2002) 1461–1506. [Google Scholar]
  19. B. Kirchheim, Deformations with finitely many gradients and stability of quasiconvex hulls. C. R. Acad. Sci. Paris Sér. I Math. 332 (2001) 289–294. [Google Scholar]
  20. B. Kirchheim, Rigidity and Geometry of Microstructures. Lectures note 16/2003, Max Planck Institute for Mathematics in the Sciences, Leipzig (2003). [Google Scholar]
  21. R.V. Kohn, New Estimates for Deformations in Terms of Their Strains. Ph.D. thesis, Princeton University, USA (1979). [Google Scholar]
  22. R.V. Kohn and S. Müller, Surface energy and microstructure in coherent phase transitions. Comm. Pure Appl. Math. 47 (1994) 405–435. [CrossRef] [MathSciNet] [Google Scholar]
  23. A. Lorent, An optimal scaling law for finite element approximations of a variational problem with non-trivial microstructure. ESAIM: M2AN 35 (2001) 921–934. [CrossRef] [EDP Sciences] [Google Scholar]
  24. M. Luskin, On the computation of crystalline microstructure. Acta Numer. 5 (1996) 191–257. [Google Scholar]
  25. P. Mattila, Geometry of Sets and Measures in Euclidean Spaces, Cambridge Studies in Advanced Mathematics 44. Cambridge University Press (1995). [Google Scholar]
  26. S. Müller, Singular perturbations as a selection criterion for periodic minimizing sequences. Calc. Var. Partial Differ. Equ. 1 (1993) 169–204. [Google Scholar]
  27. S. Müller, Variational models for microstructure and phase transitions, in Calculus of variations and geometric evolution problems (Cetraro, 1996), Lecture Notes in Mathematics 1713, Springer, Berlin (1999) 85–210. www.mis.mpg.de/cgi-bin/lecturenotes.pl. [Google Scholar]
  28. S. Müller, Uniform Lipschitz estimates for extremals of singularly perturbed nonconvex functionals. MIS MPG, Preprint 2 (1999). [Google Scholar]
  29. S. Müller and V. Šverák, Attainment results for the two-well problem by convex integration, in Geometric Analysis and the Calculus of Variations. For Stefan Hildebrandt, J. Jost Ed., International Press, Cambridge (1996) 239–251. [Google Scholar]
  30. S. Müller and V. Šverák, Convex integration with constraints and applications to phase transitions and partial differential equations. J. Eur. Math. Soc. (JEMS) 1 (1999) 393–422. [CrossRef] [MathSciNet] [Google Scholar]
  31. S. Müller and V. Šverák, Convex integration for Lipschitz mappings and counterexamples to regularity. Ann. Math. 157 (2003) 715–742. [CrossRef] [MathSciNet] [Google Scholar]
  32. S. Müller, M. Rieger and V. Šverák, Parabolic systems with nowhere smooth solutions. Arch. Rational Mech. Anal. 177 (2005) 1–20. [CrossRef] [Google Scholar]
  33. M.A. Sychev, Comparing two methods of resolving homogeneous differential inclusions. Calc. Var. Partial Differ. Equ. 13 (2001) 213–229. [CrossRef] [Google Scholar]
  34. M.A. Sychev and S. Müller, Optimal existence theorems for nonhomogeneous differential inclusions. J. Funct. Anal. 181 (2001) 447–475. [CrossRef] [MathSciNet] [Google Scholar]
  35. V. Šverák, On the problem of two wells, in Microstructure and phase transition, D. Kinderlehrer, R.D. James, M. Luskin and J. Ericksen Eds., IMA Vol. Math. Appl. 54, Springer, New York (1993) 183–189. [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.