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Existence and characterization of hydrostatic pressure in finite deformations of incompressible elastic bodies. (English) Zbl 0483.73035


MSC:

74B20 Nonlinear elasticity
74S30 Other numerical methods in solid mechanics (MSC2010)
49J99 Existence theories in calculus of variations and optimal control
46E40 Spaces of vector- and operator-valued functions
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems

Citations:

Zbl 0383.35057
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References:

[1] Babu?ka, I. and Aziz, A. K., Survey Lectures on the Mathematical Foundations of the Finite Element Method,The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, Edited by A. K., Aziz, Academic Press, NY, pp. 3-359, 1972. · Zbl 0268.65052
[2] Ball, J. M., Convexity Conditions and Existence Theorems in Nonlinear Elasticity,Archive for Rational Mechanics and Analysis, Vol. 63, No. 4 (1977) 337-403. · Zbl 0368.73040
[3] Brezzi, F., On the Existence, Uniqueness, and Approximation of Saddle-Point Problems Arising from Lagrange Multipliers,Rev. Francais Automat. Informat. Recherche Opérationelle, Sér. Rouge Anal. Numér., R-2 (1974) 129-151.
[4] Cantor, M., Perfect Fluid Flows over 357-1 with Asymptotic Conditions,Journal of Functional Analysis, Vol. 18 (1975) 73-84. · Zbl 0306.58007
[5] Cantor, M. Global Analysis over Noncompact Spaces,PhD Dissertation, The University of California, Berkeley 1973.
[6] Cesari, L., Lower Semicontinuity Theorems and Lower Closure Theorems Without Seminormality Conditions,Annali Mat. Pura. Appl., Vol. 98 (1974) 381-397. · Zbl 0281.49006
[7] Crandall, M. C. and Rabinowitz, P. H.. Bifurcation from a Simple Eigenvalues,Journal of Functional Analysis, Vol. 8 (1971) 321-340. · Zbl 0219.46015
[8] Ladyzenskaya, O. A.,The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, NY 1963.
[9] Oden, J. T. and Kikuchi, N., Existence Theory for a Class of Problems in Nonlinear Elasticity: Finite Plane Strain of a Compressible Hyperelastic Body,TICOM Report 78-13,July 1978.
[10] Temam, R.,Navier Stokes Equations, North Holland, Amsterdam 1978. · Zbl 0428.35065
[11] Vainberg, M. M.,Variational Method and Method of Monotone Operators in the Theory of Nonlinear Equations, John Wiley and Sons/Halsted Press, New York, 1973. · Zbl 0279.47022
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