References
J. M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63 (1977), pp. 337–403.
J. M. Ball, Strict convexity, strong ellipticity, and regularity in the calculus of variations, Math. Proc. Camb. Phil. Soc. 87 (1980), pp. 501–513.
J. M. Ball, Discontinuous equilibrium solutions and cavitation in nonlinear elasticity, Phil. Trans. R. Soc. (London) A 306 (1982), pp. 557–611.
J. Carr, M. E. Gurtin & M. Slemrod, One-dimensional structured phase transformations under prescribed loads, MRC Report no. 2559, Mathematics Research Center, University of Wisconsin-Madison, 1983.
B. Dacorogna, Weak continuity and weak semicontinuity of non-linear functionals, Lecture Notes in Mathematics no. 922, Springer-Verlag, Berlin, 1982.
B. Dacorogna, A relaxation theorem and its application to the equilibrium of gases, Arch. Rational Mech. Anal. 77 (1981), pp. 359–386.
B. Dacorogna, Quasiconvexity and relaxation of nonconvex problems in the calculus of variations, J. Funct. Anal. 46 (1982), pp. 102–118.
J. L. Ericksen, Equilibrium of bars, J. Elasticity 5 (1975), pp. 191–201.
M. E. Gurtin, An introduction to continuum mechanics, Academic Press, New York, 1981.
G. H. Hardy, J. E. Littlewood & G. Polya, Inequalities, Cambridge University Press, Cambridge, 1952.
C. B. Morrey, Quasi-convexity and the lower semicontinuity of multiple integrals, Pacific J. Math. 2 (1952), pp. 25–53.
J. E. Marsden & T. J. R. Hughes, Mathematical foundations of elasticity, Prentice-Hall, Englewood Cliffs, 1983.
P. Podio-Guidugli, G. Vergara Caffarelli & E. G. Virga, Discontinuous energy minimizers in nonlinear elastostatics: an example of J. Ball revisited, to appear in J. Elasticity, 1984.
C. Truesdell & R. A. Toupin, The classical field theories, Handbuch der Physik III/1, S. Flügge Ed., Springer-Verlag, Berlin, 1960.
Author information
Authors and Affiliations
Additional information
Dedicated to Walter Noll on his sixtieth birthday
Rights and permissions
About this article
Cite this article
Podio-Guiougli, P., Vergara Caffarelli, G. & Virga, E.G. Cavitation and phase transition of hyperelastic fluids. Arch. Rational Mech. Anal. 92, 121–136 (1986). https://doi.org/10.1007/BF00251253
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00251253