Free Access
Volume 38, Number 3, May-June 2004
Page(s) 397 - 418
Published online 15 June 2004
  1. J.M. Ball and R.D. James, Fine phase mixtures as minimizers of energy. Arch. Rational Mech. Anal. 100 (1987) 13–52. [Google Scholar]
  2. J.M. Ball, B. Kirchheim and J. Kristensen, Regularity of quasiconvex envelopes. Calc. Var. Partial Differential Equations 11 (2000) 333–359. [CrossRef] [MathSciNet] [Google Scholar]
  3. H. Berliocchi and J.-M. Lasry, Intégrandes normales et mesures paramétrées en calcul des variations. Bull. Soc. Math. France 101 (1973) 129–184. [MathSciNet] [Google Scholar]
  4. C. Carstensen, Numerical analysis of microstructure, in Theory and numerics of differential equations (Durham, 2000), Universitext, Springer Verlag, Berlin (2001) 59–126. [Google Scholar]
  5. C. Carstensen and P. Plecháč, Numerical solution of the scalar double-well problem allowing microstructure. Math. Comp. 66 (1997) 997–1026. [Google Scholar]
  6. C. Carstensen and T. Roubíček, Numerical approximation of Young measures in non-convex variational problems. Numer. Math. 84 (2000) 395–415. [CrossRef] [MathSciNet] [Google Scholar]
  7. C. Carstensen and G. Dolzmann, Time-space discretization of the nonlinear hyperbolic system Formula . SIAM J. Numer. Anal. 42 (2004) 75–89. [CrossRef] [MathSciNet] [Google Scholar]
  8. M. Chipot, C. Collins and D. Kinderlehrer, Numerical analysis of oscillations in multiple well problems. Numer. Math. 70 (1995) 259–282. [CrossRef] [MathSciNet] [Google Scholar]
  9. C. Collins and M. Luskin, Optimal-order error estimates for the finite element approximation of the solution of a nonconvex variational problem. Math. Comp. 57 (1991) 621–637. [CrossRef] [MathSciNet] [Google Scholar]
  10. C. Collins, D. Kinderlehrer and M. Luskin, Numerical approximation of the solution of a variational problem with a double well potential. SIAM J. Numer. Anal. 28 (1991) 321–332. [CrossRef] [MathSciNet] [Google Scholar]
  11. C.M. Dafermos and W.J. Hrusa, Energy methods for quasilinear hyperbolic initial-boundary value problems. Applications to elastodynamics. Arch. Rational Mech. Anal. 87 (1985) 267–292. [MathSciNet] [Google Scholar]
  12. S. Demoulini, Young-measure solutions for a nonlinear parabolic equation of forward-backward type. SIAM J. Math. Anal. 27 (1996) 376–403. [CrossRef] [MathSciNet] [Google Scholar]
  13. S. Demoulini, Young-measure solutions for nonlinear evolutionary systems of mixed type. Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (1997) 143–162. [CrossRef] [MathSciNet] [Google Scholar]
  14. G. Friesecke and G. Dolzmann, Implicit time discretization and global existence for a quasi-linear evolution equation with nonconvex energy. SIAM J. Math. Anal. 28 (1997) 363–380. [CrossRef] [MathSciNet] [Google Scholar]
  15. D. Kinderlehrer and P. Pedregal, Weak convergence of integrands and the Young measure representation. SIAM J. Math. Anal. 23 (1992) 1–19. [CrossRef] [MathSciNet] [Google Scholar]
  16. P. Klouček and M. Luskin, The computation of the dynamics of the martensitic transformation. Contin. Mech. Thermodyn. 6 (1994) 209–240. [CrossRef] [MathSciNet] [Google Scholar]
  17. M. Luskin, On the computation of crystalline microstructure, in Acta numerica, Cambridge Univ. Press, Cambridge (1996) 191–257. [Google Scholar]
  18. S. Müller, Variational models for microstructure and phase transition, in Calculus of Variations and Geometric Evolution Problems, S. Hildebrandt and M. Struwe Eds., Lect. Notes Math. 1713, Springer-Verlag, Berlin (1999). [Google Scholar]
  19. R.A. Nicolaides and N.J. Walkington, Computation of microstructure utilizing Young measure representations, in Transactions of the Tenth Army Conference on Applied Mathematics and Computing (West Point, NY, 1992), US Army Res. Office, Research Triangle Park, NC (1993) 57–68. [Google Scholar]
  20. P. Pedregal, Parametrized measures and variational principles. Birkhäuser (1997). [Google Scholar]
  21. M.O. Rieger, Time dependent Young measure solutions for an elasticity equation with diffusion, in International Conference on Differential Equations, Vol. 2 (Berlin, 1999), World Sci. Publishing, River Edge, NJ 1 (2000) 457–459. [Google Scholar]
  22. M.O. Rieger, Young-measure solutions for nonconvex elastodynamics. SIAM J. Math. Anal. 34 (2003) 1380–1398. [CrossRef] [MathSciNet] [Google Scholar]
  23. M.O. Rieger and J. Zimmer, Global existence for nonconvex thermoelasticity. Preprint 30/2002, Center for Nonlinear Analysis, Carnegie Mellon University, Pittsburgh, USA (2002). [Google Scholar]
  24. T. Roubíček, Relaxation in optimization theory and variational calculus. Walter de Gruyter & Co., Berlin (1997). [Google Scholar]
  25. M. Slemrod, Dynamics of measured valued solutions to a backward-forward heat equation. J. Dynam. Differ. Equations 3 (1991) 1–28. [CrossRef] [Google Scholar]
  26. L. Tartar, Compensated compactness and applications to partial differential equations, in Nonlinear analysis and mechanics: Heriot-Watt Symposium. Pitman, Boston, Mass. IV (1979) 136–212. [Google Scholar]
  27. M.E. Taylor, Partial Differential Equations III. Appl. Math. Sciences. Springer-Verlag, 117 (1996). [Google Scholar]
  28. L.C. Young, Generalized curves and the existence of an attained absolute minimum in the calculus variations, volume classe III. (1937). [Google Scholar]
  29. L.C. Young, Lectures on the calculus of variations and optimal control theory. W.B. Saunders Co., Philadelphia (1969). [Google Scholar]
  30. K. Zhang, On some semiconvex envelopes. NoDEA. Nonlinear Differential Equations Appl. 9 (2002) 37–44. [CrossRef] [MathSciNet] [Google Scholar]

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