Characterization of Convex Isotropic Functions

1. J.M. Ball, Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rat. Mech. Anal. 63 (1977) 337–403.

   Article  MATH  Google Scholar 

2. J.M. Ball, Differentiability properties of symmetric and isotropic functions. Duke Math. J. 51 (1984) 699–728.

   Article  MATH  MathSciNet  Google Scholar 

3. H. Busemann, G. Ewald and G.C., Sheppard, Convex bodies and convexity on Grassmann cones. Parts I–IV, Math. Ann. 151 (1963) 1–41.

   Article  MATH  MathSciNet  Google Scholar 

4. P.G. Ciarlet, Mathematical Elasticity, Vol. I, North-Holland, Amsterdam (1988).

   MATH  Google Scholar 

5. B.D. Coleman and W. Noll, On the thermostatics of continuous media. Arch. Rat. Mech. Anal. 4 (1959) 97–128.

   Article  MATH  MathSciNet  Google Scholar 

6. B. Dacorogna, Direct Methods in the Calculus of Variations, Springer-Verlag, Berlin (1990).

   MATH  Google Scholar 

7. P. Rosakis and H.C. Simpson, On the relation between polyconvexity and rank-one convexity in nonlinear elasticity. J. Elasticity 37 (1995) 113–137.

   Article  MATH  MathSciNet  Google Scholar 

8. J. von Neumann, Some matrix-inequalities and metrization of matrix-space, Tomsk Univ. Rev., 1 (1937) 286–300.

   MATH  Google Scholar 

9. M. Šilhavý, Convexity conditions for rotationally invariant functions in two dimensions. preprint.

10. M. Šilhavý, The Mechanics and Thermodynamics of Continuous Media, Springer, Berlin (1997).

    MATH  Google Scholar 

11. J.E. Dunn and R. Fosdick, The Weierstrass condition for a special class of elastic materials. J. Elasticity 34 (1994) 167–184.

    MATH  MathSciNet  Google Scholar 

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