Volume 15, Number 2, April-June 2009
|Page(s)||322 - 366|
|Published online||24 June 2008|
- L. Ambrosio, A. Coscia and G. Dal Maso, Fine properties of functions with bounded deformation. Arch. Rational Mech. Anal. 139 (1997) 201–238. [CrossRef] [MathSciNet]
- 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).
- J.M. Ball and R.D. James, Fine phase mixtures as minimisers of energy. Arch. Rational Mech. Anal. 100 (1987) 13–52. [CrossRef] [MathSciNet]
- 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. [CrossRef]
- M. Chipot, The appearance of microstructures in problems with incompatible wells and their numerical approach. Numer. Math. 83 (1999) 325–352. [CrossRef] [MathSciNet]
- M. Chipot and D. Kinderlehrer, Equilibrium configurations of crystals. Arch. Rational Mech. Anal. 103 (1988) 237–277. [MathSciNet]
- 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.
- S. Conti, Branched microstructures: scaling and asymptotic self-similarity. Comm. Pure Appl. Math. 53 (2000) 1448–1474. [CrossRef] [MathSciNet]
- S. Conti and B. Schweizer, Rigidity and Gamma convergence for solid-solid phase transitions with -invariance. Comm. Pure Appl. Math. 59 (2006) 830–868. [CrossRef] [MathSciNet]
- S. Conti, D. Faraco and F. Maggi, A new approach to counterexamples to estimates: Korn's inequality, geometric rigidity, and regularity for gradients of separately convex functions. Arch. Rational Mech. Anal. 175 (2005) 287–300. [CrossRef] [MathSciNet]
- 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]
- 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]
- C. De Lellis and L. Székelyhidi, The Euler equations as a differential inclusion. Ann. Math. (to appear).
- 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]
- G. Dolzmann and B. Kirchheim, Liquid-like behavior of shape memory alloys. C. R. Math. Acad. Sci. Paris 336 (2003) 441–446. [CrossRef] [MathSciNet]
- G. Dolzmann and S. Müller, Microstructures with finite surface energy: the two-well problem. Arch. Rational Mech. Anal. 132 (1995) 101–141. [CrossRef] [MathSciNet]
- L.C. Evans and R.F. Gariepy, Measure theory and fine properties of functions, Studies in Advanced Mathematics. CRC Press, Boca Raton, FL (1992).
- 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. [CrossRef] [MathSciNet]
- B. Kirchheim, Deformations with finitely many gradients and stability of quasiconvex hulls. C. R. Acad. Sci. Paris Sér. I Math. 332 (2001) 289–294.
- B. Kirchheim, Rigidity and Geometry of Microstructures. Lectures note 16/2003, Max Planck Institute for Mathematics in the Sciences, Leipzig (2003).
- R.V. Kohn, New Estimates for Deformations in Terms of Their Strains. Ph.D. thesis, Princeton University, USA (1979).
- R.V. Kohn and S. Müller, Surface energy and microstructure in coherent phase transitions. Comm. Pure Appl. Math. 47 (1994) 405–435. [CrossRef] [MathSciNet]
- 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]
- M. Luskin, On the computation of crystalline microstructure. Acta Numer. 5 (1996) 191–257. [CrossRef]
- P. Mattila, Geometry of Sets and Measures in Euclidean Spaces, Cambridge Studies in Advanced Mathematics 44. Cambridge University Press (1995).
- S. Müller, Singular perturbations as a selection criterion for periodic minimizing sequences. Calc. Var. Partial Differ. Equ. 1 (1993) 169–204. [CrossRef]
- 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.
- S. Müller, Uniform Lipschitz estimates for extremals of singularly perturbed nonconvex functionals. MIS MPG, Preprint 2 (1999).
- 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.
- 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]
- S. Müller and V. Šverák, Convex integration for Lipschitz mappings and counterexamples to regularity. Ann. Math. 157 (2003) 715–742. [CrossRef] [MathSciNet]
- S. Müller, M. Rieger and V. Šverák, Parabolic systems with nowhere smooth solutions. Arch. Rational Mech. Anal. 177 (2005) 1–20. [CrossRef]
- M.A. Sychev, Comparing two methods of resolving homogeneous differential inclusions. Calc. Var. Partial Differ. Equ. 13 (2001) 213–229. [CrossRef]
- M.A. Sychev and S. Müller, Optimal existence theorems for nonhomogeneous differential inclusions. J. Funct. Anal. 181 (2001) 447–475. [CrossRef] [MathSciNet]
- 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.
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