Archive for Rational Mechanics and Analysis

, Volume 90, Issue 3, pp 195–212 | Cite as

The existence of the flux vector and the divergence theorem for general Cauchy fluxes

  • Miroslav Šilhavy


Neural Network Complex System Nonlinear Dynamics Electromagnetism Divergence Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. E. Gurtin & L. C. Martins, Cauchy's theorem in classical physics, Arch. Rational Mech. Anal. 60 (1976), 305–324.Google Scholar
  2. 2.
    L. C. Martins, On Cauchy's theorem in classical physics: some counterexamples, Arch. Rational Mech. Anal. 60 (1976), 325–328.Google Scholar
  3. 3.
    W. P. Ziemer, Cauchy flux and sets of finite perimeter, Arch. Rational Mech. Anal. 84 (1983), 189–201.Google Scholar
  4. 4.
    A. L. Cauchy, Recherches sur l'équilibre et le mouvement intérieur des corps solides ou fluides, élastiques ou non-élastiques, Bull. Soc. Philomath. (1823), 9–13.Google Scholar
  5. 5.
    W. Noll, The foundations of classical mechanics in the light of recent advances in continuum mechanics, pp. 266–281 of The Axiomatic Method, with Special Reference to Geometry and Physics (Symposium at Berkley, 1957). Amsterdam: North-Holland Publishing Co. 1959.Google Scholar
  6. 6.
    W. Noll, Lectures on the foundations of continuum mechanics. Arch. Rational Mech. Anal. 52 (1973), 62–92.Google Scholar
  7. 7.
    W. Noll, The foundations of mechanics, in Nonlinear Continuum Theories, C.I.M.E. Lectures, Roma 1966.Google Scholar
  8. 8.
    M. E. Gurtin & W. O. Williams, An axiomatic foundation for continuum thermodynamics, Arch. Rational. Mech. Anal. 26 (1967), 83–117.Google Scholar
  9. 9.
    M. E. Gurtin, V. J. Mizel, & W. O. Williams, A note on Cauchy's stress theorem, J. Math. Anal. Appl. 22 (1968), 398–401.Google Scholar
  10. 10.
    W. Rudin, Real and Complex Analysis, McGraw-Hill, New York 1966.Google Scholar
  11. 11.
    H. Federer, Geometric measure theory, Springer-Verlag, New York 1969.Google Scholar
  12. 12.
    C. Banfi & M. Fabrizio, Sul concetto di sottocorpo nella meccanica dei continui, Rend. Acc. Naz. Lincei, 66 (1979), 136–142.Google Scholar
  13. 13.
    C. Banfi & M. Fabrizio, Global theory for thermodynamic behaviour of a continuous medium, Ann. Univ. Ferrara 27 (1981), 181–199.Google Scholar
  14. 14.
    G. Birkhoff & J. Von Neumann, The logic of quantum mechanics, Annals of Math. 37 (1936), 823–843.Google Scholar
  15. 15.
    B. Fuglede, On a theorem of F. Riesz, Math. Scand. 3 (1955) 283–302.Google Scholar
  16. 16.
    I. Ekeland & R. Temam, Convex Analysis and Variational Problems, Amsterdam, North-Holland Publishing Co. 1976.Google Scholar

Copyright information

© Springer-Verlag GmbH & Co 1985

Authors and Affiliations

  • Miroslav Šilhavy
    • 1
  1. 1.Mathematical InstituteCzechoslovak Academy of SciencesPrague

Personalised recommendations