Book Review

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MathSciNet review: 1567869

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Book Information:

Author: 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.

*Existence of solutions of the equilibrium equations for non-linearly elastic rings and arches*, Indiana Univ. Math. J.

**20**(1970/71), 281–302. MR

**266478**, DOI 10.1512/iumj.1970.20.20025

*Regular and singular problems for large elastic deformations of tubes, wedges, and cylinders*, Arch. Rational Mech. Anal.

**83**(1983), no. 1, 1–52. MR

**695361**, DOI 10.1007/BF00281086

*Convexity conditions and existence theorems in nonlinear elasticity*, Arch. Rational Mech. Anal.

**63**(1976/77), no. 4, 337–403. MR

**475169**, DOI 10.1007/BF00279992

*Global invertibility of Sobolev functions and the interpenetration of matter*, Proc. Roy. Soc. Edinburgh Sect. A

**88**(1981), no. 3-4, 315–328. MR

**616782**, DOI 10.1017/S030821050002014X

**5.**

*On the existence and uniqueness of solutions to boundary value problems in finite elasticity*, Thesis, Carnegie-Mellon University, Pittsburgh, 1968.

*Symmetry and bifurcation in three-dimensional elasticity. I*, Arch. Rational Mech. Anal.

**80**(1982), no. 4, 295–331. MR

**677564**, DOI 10.1007/BF00253119

*Symmetry and bifurcation in three-dimensional elasticity. II*, Arch. Rational Mech. Anal.

**83**(1983), no. 4, 363–395. MR

**714980**, DOI 10.1007/BF00963840

*Mathematical elasticity. Vol. I*, Studies in Mathematics and its Applications, vol. 20, North-Holland Publishing Co., Amsterdam, 1988. Three-dimensional elasticity. MR

**936420**

*A justification of the two-dimensional linear plate model*, J. Mécanique

**18**(1979), no. 2, 315–344 (English, with French summary). MR

**533827**

*Unilateral problems in nonlinear, three-dimensional elasticity*, Arch. Rational Mech. Anal.

**87**(1985), no. 4, 319–338 (English, with French summary). MR

**767504**, DOI 10.1007/BF00250917

*Injectivity and self-contact in nonlinear elasticity*, Arch. Rational Mech. Anal.

**97**(1987), no. 3, 171–188. MR

**862546**, DOI 10.1007/BF00250807

*On the thermostatics of continuous media*, Arch. Rational Mech. Anal.

**4**(1959), 97–128 (1959). MR

**109527**, DOI 10.1007/BF00281381

*On the impossibility of linear Cauchy and Piola-Kirchhoff constitutive theories for stress in solids*, J. Elasticity

**9**(1979), no. 1, 83–89. MR

**528599**, DOI 10.1007/BF00040982

*An introduction to continuum mechanics*, Mathematics in Science and Engineering, vol. 158, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR

**636255**

*Structure of the set of equilibrated loads in nonlinear elasticity and applications to existence and nonexistence*, J. Elasticity

**17**(1987), no. 2, 123–141 (English, with French summary). MR

**885602**, DOI 10.1007/BF00043020

*Topics in the mathematical foundations of elasticity*, Nonlinear analysis and mechanics: Heriot-Watt Symposium, Vol. II, Res. Notes in Math., vol. 27, Pitman, Boston, Mass.-London, 1978, pp. 30–285. MR

**576233**

**17.**

*Mathematical foundations of elasticity*, Prentice-Hall, Englewood Cliffs, 1983.

*Un teorema di esistenza ed unicità relativo alle equazioni dell’elastostatica isoterma per deformazioni finite*, Ricerche Mat.

**3**(1954), 247–267 (Italian). MR

**74237**

*The non-linear field theories of mechanics*, Handbuch der Physik, Band III/3, Springer-Verlag, Berlin, 1965. MR

**0193816**

*Local theorems of existence and uniqueness in finite elastostatics*, Proceedings of the IUTAM Symposium on Finite Elasticity (Bethlehem, Pa., 1980) Nijhoff, The Hague, 1982, pp. 401–421. MR

**676677**

**21.**

*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.

*The differentiability of an operator connected with a class of quasilinear differential systems*, Rend. Sem. Mat. Univ. Padova

**57**(1977), 311–322 (1978) (Italian, with English summary). MR

**526198**

*Introduction to rational elasticity*, Monographs and Textbooks on Mechanics of Solids and Fluids, Mechanics of Continua, Noordhoff International Publishing, Leyden, 1973. MR

**0468442**

Review Information:

Reviewer: Philippe G. Ciarlet

Journal: Bull. Amer. Math. Soc.

**23**(1990), 209-222

DOI: https://doi.org/10.1090/S0273-0979-1990-15934-8