A class of fit regions and a universe of shapes for continuum mechanics

Journal of Elasticity

Volumn 70, Issue 1-3, 2003, Pages 175-195

  Del Piero, Gianpietro ^a  

^a UNIVERSITY OF FERRARA   (Italy)

Author keywords

Fit regions; Foundations of continuum mechanics; Universes of bodies

Indexed keywords

BOUNDARY CONDITIONS; CONFORMAL MAPPING; EQUIVALENCE CLASSES; KINEMATICS; SET THEORY; THEOREM PROVING;

FIT REGIONS; HAUSDORFF MEASURE; LEBESGUE MEASURE; UNIVERSES OF BODIES;

CONTINUUM MECHANICS;

EID: 0346255332     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:ELAS.0000005551.92536.c6     Document Type: Article

References (16)

1. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Oxford Science Publications, Oxford (2000).
2. C. Banfi and M. Fabrizio, Sul concetto di sottocorpo nella meccanica dei continui. Rend. Accad. Naz. Lincei 66 (1979) 136-142.
3. M. Degiovanni, A. Marzocchi and A. Musesti, Cauchy fluxes associated with tensor fields having divergence measure. Arch. Rational Mech. Anal. 147 (1999) 197-223.
4. J. Dixmier, General Topology, Springer Undergraduate Texts in Mathematics. Springer, New York (1984).
5. L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions, CRC Press, Boca Ralton, FL (1992).
6. M.E. Gurtin, Private communication, Blacksburg (June 2002).
7. M.E. Gurtin, W.O. Williams and W.P. Ziemer, Geometric measure theory and the axioms of continuum thermodynamics. Arch. Rational Mech. Anal. 92 (1986) 1-22.
8. W. Noll, La ménique classique, basée sur un axiome d'objectivité. In: La Méthode Axiomatique dans les Mécaniques Classiques et Nouvelles, Colloque International, Paris, 1959. Gauthier-Villars, Paris (1963).
9. W. Noll, The foundations of mechanics. In: Non-linear Continuum Theories, CIME Lecture, 1965. Cremonese, Roma (1966), pp. 159-200.
10. W. Noll, Lectures on the foundations of continuum mechanics and thermodynamics. Arch. Rational Mech. Anal. 52 (1973) 62-92.
11. W. Noll, Continuum Mechanics and geometric integration theory. In: F.W. Lawvere and S.H. Schnauel (eds), Categories in Continuum Physics, Buffalo, 1982, Springer Lecture Notes in Mathematics, Vol. 1174. Springer, Berlin (1986) pp. 17-29.
12. W. Noll and E.G. Virga, Fit regions and functions of bounded variation. Arch. Rational Mech. Anal. 102 (1988) 1-21.
13. M. Šilhavý, The existence of the flux vector and the divergence theorem for general Cauchy fluxes. Arch. Rational Mech. Anal. 90 (1985) 195-212.
14. p. Arch. Rational Mech. Anal. 116 (1991) 223-255.
15. C.A. Truesdell, A First Course in Rational Continuum Mechanics, Vol. 1, 2nd edn. Academic Press, Boston (1991).
16. A.I. Vol'pert and S.I. Hudjaev, Analysis in Classes of Discontinuous Functions and Equations of Mathematical Physics. Nijhoff, Dordrecht (1985).