Linear deformations as global minimizers in nonlinear elasticity
Author:
Scott J. Spector
Journal:
Quart. Appl. Math. 52 (1994), 59-64
MSC:
Primary 73C50; Secondary 49K10, 73G05, 73V25
DOI:
https://doi.org/10.1090/qam/1262319
MathSciNet review:
MR1262319
Full-text PDF Free Access
References |
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Additional Information
J. M. Ball, Constitutive inequalities and existence theorems in nonlinear elastostatics, Nonlinear Analysis and Mechanics, Vol. I (R. J. Knops, Ed.) London: Pitman, 1977
J. M. Ball, Discontinuous equilibrium solutions and cavitation in nonlinear elasticity, Phil. Trans. Roy. Soc. London A 306, 557–611 (1982)
J. M. Ball and F. Murat, $W^{1, p}$-quasiconvexity and variational problems for multiple integrals, J. Func. Anal. 58, 225–253 (1984)
L. C. Evans and R. E. Gariepy, Lecture Notes on Measure Theory and Fine Properties of Functions, Boca Raton: CRC Press, 1992
H. Federer, Geometric Measure Theory, New York, Springer, 1969
R. D. James and S. J. Spector, The formation of filamentary voids in solids, J. Mech. Phys. Solids 39, 783–813 (1991)
R. D. James and S. J. Spector, Remarks on $W^{1, p}$-quasiconvexity, interpenetration of matter, and function spaces for elasticity, Anal. Non Linéaire 9, 263–280 (1992)
R. J. Knops, and C. A. Stuart, Quasiconvexity and uniqueness of equilibrium solutions in nonlinear elasticity, Arch. Rational Mech. Anal. 86, 233–249 (1984)
C. B. Morrey, Multiple Integrals in the Calculus of Variations, New York, Springer, 1966
S. Müller, S. Spector, and Tang Qi, Invertibility and a topological property of Sobolev maps, Preprint
V. Šverák, Regularity properties of deformations with finite energy, Arch. Rational Mech. Anal. 100, 105–127 (1988)
J. M. Ball, Constitutive inequalities and existence theorems in nonlinear elastostatics, Nonlinear Analysis and Mechanics, Vol. I (R. J. Knops, Ed.) London: Pitman, 1977
J. M. Ball, Discontinuous equilibrium solutions and cavitation in nonlinear elasticity, Phil. Trans. Roy. Soc. London A 306, 557–611 (1982)
J. M. Ball and F. Murat, $W^{1, p}$-quasiconvexity and variational problems for multiple integrals, J. Func. Anal. 58, 225–253 (1984)
L. C. Evans and R. E. Gariepy, Lecture Notes on Measure Theory and Fine Properties of Functions, Boca Raton: CRC Press, 1992
H. Federer, Geometric Measure Theory, New York, Springer, 1969
R. D. James and S. J. Spector, The formation of filamentary voids in solids, J. Mech. Phys. Solids 39, 783–813 (1991)
R. D. James and S. J. Spector, Remarks on $W^{1, p}$-quasiconvexity, interpenetration of matter, and function spaces for elasticity, Anal. Non Linéaire 9, 263–280 (1992)
R. J. Knops, and C. A. Stuart, Quasiconvexity and uniqueness of equilibrium solutions in nonlinear elasticity, Arch. Rational Mech. Anal. 86, 233–249 (1984)
C. B. Morrey, Multiple Integrals in the Calculus of Variations, New York, Springer, 1966
S. Müller, S. Spector, and Tang Qi, Invertibility and a topological property of Sobolev maps, Preprint
V. Šverák, Regularity properties of deformations with finite energy, Arch. Rational Mech. Anal. 100, 105–127 (1988)
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Article copyright:
© Copyright 1994
American Mathematical Society
