References on variational models and weak convergence methods for crystalline solids (for AMSC 698V) - B. Li

AMSC 698V: Advanced Topics in Applied Mathematics, Fall, 2003

MATHEMATICAL AND COMPUTATIONAL PROBLEMS
IN MATERIALS SCIENCE

Instructor: Bo Li

References on Variational Models and Weak Convergence Methods for Crystalline solids


  1. E. Acerbi and N. Fusco, Semicontinuity problems in the calculus of variations, Arch. Rat. Mech. Anal., 86:125-145, 1986.
  2. E. Acerbi and N. Fusco, A regularity theorem for minimizers of quasiconvex integrals, Arch. Rat. Mech. Anal., 99:261-281, 1987.
  3. J. M. Ball, Convexity conditions and existence theorems in nonlinear elasticity}, Arch. Rat. Mech. Anal., 63:337-403, 1977.
  4. J. M. Ball, A version of the fundamental theorem for Young measures, in Partial Differential Equations and Continuum Models of Phase Transition, M. Rascle, D. Serre, and M. Slemrod, eds., Lecture Notes in Physics 344, Springer-Verlag, Berlin, 207-215, 1989.
  5. J. M. Ball, J. C. Currie, and P. J. Olver, Null Lagrangians, weak continuity and variational problems of arbitrary order, J. Funct. Anal., 41:135-174, 1981.
  6. J. Ball and F. Murat, W^{1,p}-Quasiconvexity and variational problems for multiple integrals, J. Funct. Anal., 58:225-253, 1984.
  7. J. M. Ball and R. D. James, Fine phase mixtures as minimizers of energy, Arch. Rat. Mech. Anal., 100:13-52, 1987.
  8. 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. Lond. A, 338:389-450, 1992.
  9. K. Bhattacharya, N. Firoozye, R. D. James, and R. V. Kohn, Restrictions on microstructure, Proc. Roy. Soc. Edinburgh, 124A:843-878, 1994.
  10. M. Chipot and D. Kinderlehrer, Equilibrium configurations of crystals}, Arch. Rat. Mech. Anal., 103:237-277, 1988.
  11. B. Dacorogna, Direct Methods in the Calculus of Variations, Springer-Verlag, Berlin, 1989.
  12. L. C. Evans, Quasi-convexity and partial regularity in the calculus of variations, Arch. Rat. Mech. Anal., 95:227-252, 1986.
  13. L. C. Evans, Weak Convergence Methods for Nonlinear Partial Differential Equations, CBMS Regional Conference Series in Mathematics 74, Amer. Math. Soc., Providence, RI, 1990.
  14. R. D. James and D. Kinderlehrer, Theory of diffusionless phase transitions, in Partial Differential Equations and Continuum Models of Phase Transition, M. Rascle, D. Serre, and M. Slemrod, eds., Lecture Notes in Physics 344, Springer-Verlag, Berlin, 51-84, 1989.
  15. D. Kinderlehrer and P. Pedregal, Characterizations of gradient Young measures, Arch. Rat. Mech. Anal., 115:329-365, 1991.
  16. R. V. Kohn, Relaxation of a double-well energy, Cont. Mech. Thermodyn., 3:193-236, 1991.
  17. N. G. Meyers, Quasi-convexity and lower semicontinuity in the multiple variational integrals of any order, Trans. Amer. Math. Soc., 119:125-149, 1965.
  18. C. B. Morrey, Jr., Quasiconvexity and the lower semicontinuity of multiple integrals, Pacific J. Math., 2:25-53, 1952.
  19. C. B. Morrey, Jr., Multiple Integrals in the Calculus of Variations, Springer-Verlag, 1966.
  20. L. Tartar, Compensated compactness and applications to partial differential equations, in Nonlinear Analysis and Mechanics, Heriot-Watt Symposium IV, R. Knops, ed., Pitman Research Notes in Mathematics 39, Pitman, Boston, 136-212, 1979.
  21. V. SverŠk, Rank-one convexity does not imply quasiconvexity, Proc. Roy. Soc. Edinburgh, 120A:185-189, 1992.
  22. V. SverŠk, On the problem of two wells, in Microstructure and Phase Transition, J. Ericksen, R. James, D. Kinderlehrer, and M. Luskin, eds., IMA Volumes in Mathematics and Its Applications 54, Springer-Verlag, 183-190, 1993.
  23. V. SverŠk, Lower-semicontinuity of variational integrals and compensated compactness, in Proceedings ICM 94, Birkhšuser, Z‹rich, 1995.