The calculus of variations and materials science
Author:
J. M. Ball
Journal:
Quart. Appl. Math. 56 (1998), 719-740
MSC:
Primary 49J10; Secondary 74B20, 74G65
DOI:
https://doi.org/10.1090/qam/1668735
MathSciNet review:
MR1668735
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Abstract: A review is given of the development and present state of the calculus of variations, starting from the problem of the brachistochrone, and emphasizing the current interaction with problems of materials science.
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J. M. Ball and C. Carstensen, Hadamard’s compatibility condition for microstructures, to appear
J. M. Ball and C. Carstensen, Nonclassical austenite-martensite interfaces, J. de Physique IV, to appear
J. M. Ball, C. Chu, and R. D. James, Metastability and martensite, in preparation
J. M. Ball, C. Chu, and R. D. James, Hysteresis during stress-induced variant rearrangement, J. de Physique IV, C8, 245–251 (1995)
J. M. Ball, J. C. Currie, and P. J. Olver, Null Lagrangians, weak continuity, and variational problems of arbitrary order, J. Functional Anal. 41, 135–174 (1981)
J. M. Ball, P. J. Holmes, R. D. James, R. L. Pego, and P. J. Swart, On the dynamics of fine structure, J. Nonlinear Sci. 1, 17–90 (1991)
J. M. Ball and R. D. James, From Microscales to Macroscales in Materials, book in preparation
J. M. Ball and R. D. James, The fundamental sufficiency theorem of the one-dimensional calculus of variations, in preparation
J. M. Ball and R. D. James, Young measure disjoint sets of gradients and metastability, in preparation
J. M. Ball and R. D. James, Fine phase mixtures as minimizers of energy, Arch. Rat. Mech. Anal. 100, 13–52 (1987)
J. M. Ball and R. D. James, A characterization of plane strain, Proc. Roy. Soc. London A 432, 93–99 (1991)
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