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Book Information

Author(s): T. Valent
Title: Boundary value problems of finite elasticity
Additional book information: Springer-Verlag, Heidelberg, 1988, xii+192 pp., $64.00. ISBN 0-387-96550-5

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4.: J. Ball, Global invertibility of Sobolev functions and the interpenetration of matter, Proc. Roy. Soc. Edinburgh 88A (1981), 315-328. MR 616782
5.: M. van Buren, On the existence and uniqueness of solutions to boundary value problems in finite elasticity, Thesis, Carnegie-Mellon University, Pittsburgh, 1968.
6.: D. R. J. Chillingworth and J. E. Marsden, Symmetry and bifurcation in three-dimensional elasticity, Part I, Arch. Rational Mech. Anal. 80 (1982), 295-331. MR 677564
7.: D. R. J. Chillingworth and J. E. Marsden, Symmetry and bifurcation in three-dimensional elasticity, Part II, Arch. Rational Mech. Anal. 83 (1983), 363-395. MR 714980
8.: P. G. Ciarlet, Mathematical elasticity, Vol. I: Three-dimensional elasticity, North-Holland, Amsterdam, 1988. MR 936420
9.: P. G. Ciarlet and P. Destuynder, A justification of a nonlinear model in plate theory, Comput. Methods Appl. Mech. Engrg. 17/18 (1979), 227-258. MR 533827
10.: P. G. Ciarlet and J. Nečas, Unilateral problems in nonlinear, three-dimensional elasticity, Arch. Rational Mech. Anal. 87 (1985), 319-338. MR 767504
11.: P. G. Ciarlet and J. Nečas, Injectivity and self-contact in nonlinear elasticity, Arch Rational Mech. Anal. 19 (1987), 171-188. MR 862546
12.: B. D. Coleman and W. Noll, On the thermostatics of continuous media, Arch. Rational Mech. Anal. 4 (1959), 97-128. MR 109527
13.: R. L. Fosdick and J. Serrin, On the impossibility of linear Cauchy and Piola-Kirchhoff constitutive theories for stress in solids, J. Elasticity 9 (1979), 83-89. MR 528599
14.: M. E. Gurtin, In introduction to continuum mechanics, Academic Press, New York, 1981. MR 636255
15.: H. Le Dret, Structure of the set of equilibrated loads in nonlinear elasticity and applications to existence and nonexistence, J. Elasticity 17 (1987), 123-141. MR 885602
16.: J. E. Marsden and T. J. R. Hughes, Topics in the mathematical foundations of elasticity, in Nonlinear analysis and mechanics: Heriot-Watt symposium, Vol. 2, Pitman, London, 1978, pp. 30-285. MR 576233
17.: J. E. Marsden and T. J. R. Hughes, Mathematical foundations of elasticity, Prentice-Hall, Englewood Cliffs, 1983.
18.: F. Stoppelli, Un teorema di esistenza e di unicità relativo alle equazioni dell'elastostatica isoterma per deformazioni finite, Ricerche Mat. 3 (1954), 247-267. MR 74237
19.: C. Truesdell and W. Noll, The non-linear field theories of mechanics, in Handbuch der Physik, Vol. III/3 (S. Flügge, Editor), Springer-Verlag, Berlin, 1965, pp. 1-602. MR 193816
20.: T. Valent, Local theorems of existence and uniqueness infinite elastostatics, in Finite elasticity (D. E. Carlson and R. T. Shield, Editors), Nijhoff, The Hague, 1978, pp. 401-421. MR 676677
21.: T. Valent, Pressure boundary problems infinite elasticity. Results on local existence, uniqueness and analyticity, in Proceedings, meeting on finite thermoelasticity (G. Grioli, Editor), Accademia Nazionale dei Lincei, Roma, 1986, pp. 241-264.
22.: T. Valent and G. Zampieri, Sulla differenziabilità di un operatore legato a una classe di sistemi differenziali quasi-lineari, Rend. Sem. Mat. Univ. Padova 57 (1977), 311-322. MR 526198
23.: C.-C. Wang and C. Truesdell, Introduction to rational elasticity, Noordhoff, Groningen, 1973. MR 468442

Review Information:
Journal: Bull. Amer. Math. Soc. 23 (1990), 209-222.
DOI: 10.1090/S0273-0979-1990-15934-8
PII: S 0273-0979(1990)15934-8

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ISSN 1088-9485(e) ISSN 0273-0979(p)

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