Divergence measure fields and Cauchy's stress theorem
Rendiconti del Seminario Matematico della Università di Padova, Tome 113 (2005), pp. 15-45 
@article{RSMUP_2005__113__15_0,
     author = {Silhavy, Miroslav},
     title = {Divergence measure fields and {Cauchy's} stress theorem},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {15--45},
     year = {2005},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {113},
     mrnumber = {2168979},
     zbl = {1167.74317},
     language = {en},
     url = {https://www.numdam.org/item/RSMUP_2005__113__15_0/}
}
TY  - JOUR
AU  - Silhavy, Miroslav
TI  - Divergence measure fields and Cauchy's stress theorem
JO  - Rendiconti del Seminario Matematico della Università di Padova
PY  - 2005
SP  - 15
EP  - 45
VL  - 113
PB  - Seminario Matematico of the University of Padua
UR  - https://www.numdam.org/item/RSMUP_2005__113__15_0/
LA  - en
ID  - RSMUP_2005__113__15_0
ER  - 
%0 Journal Article
%A Silhavy, Miroslav
%T Divergence measure fields and Cauchy's stress theorem
%J Rendiconti del Seminario Matematico della Università di Padova
%D 2005
%P 15-45
%V 113
%I Seminario Matematico of the University of Padua
%U https://www.numdam.org/item/RSMUP_2005__113__15_0/
%G en
%F RSMUP_2005__113__15_0
Silhavy, Miroslav. Divergence measure fields and Cauchy's stress theorem. Rendiconti del Seminario Matematico della Università di Padova, Tome 113 (2005), pp. 15-45. https://www.numdam.org/item/RSMUP_2005__113__15_0/

[1] S. S. Antman - J. E. Osborn, The principle of virtual work and integral laws of motion, Arch. Rational Mech. Anal., 69 (1979), pp. 231-262. | Zbl | MR

[2] G. Anzellotti, Pairings between measures and bounded functions and compensated compactness, Ann. Mat. Pura Appl., 135 (1983), pp. 293-318. | Zbl | MR

[3] C. Banfi - M. Fabrizio, Sul concetto di sottocorpo nella meccanica dei continui, Rend. Acc. Naz. Lincei, 66 (1979), pp. 136-142. | Zbl | MR

[4] G.-Q. Chen - H. Frid, On the Theory of Divergence-Measure Fields and Its Applications, Boletim da Sociedade Brasileira de Matemática (Bol. Soc. Bras. Math.), 32 (2001), pp. 1-33. | Zbl | MR

[5] G.-Q. Chen - H. Frid, Extended Divergence-Measure Fields and the Euler Equations for Gas Dynamics, Communications in Mathematical Physics, 236 (2003), pp. 251-280. | Zbl | MR

[6] G.-Q. Chen - H. Frid, Divergence-Measure Fields and Hyperbolic Conservation Laws, Arch. Rational Mech. Anal., 147 (1999), pp. 89-118. | Zbl | MR

[7] M. Degiovanni - A. Marzocchi - A. Musesti, Cauchy fluxes associated with tensor fields having divergence measure, Arch. Rational Mech. Anal., 147 (1999), pp. 197-223. | Zbl | MR

[8] N. Dunford - J. T. Schwartz, Linear Operators: Part I: General Theory, New York, Willey (1958). | Zbl | MR

[9] K. Falconer, Fractal geometry, Chichester, Willey (1990). | Zbl | MR

[10] H. Federer, Geometric measure theory, New York, Springer (1969). | Zbl | MR

[11] R. Fosdick - E. Virga, A variational proof of the stress theorem of Cauchy, Arch. Rational Mech. Anal., 105 (1989), pp. 95-103. | Zbl | MR

[12] R. V. Kohn - R. Temam, Dual spaces of stresses and strains, Appl. Math. Optimization, 10 (1983), pp. 1-35. | Zbl | MR

[13] M. E. Gurtin - L. C. Martins, Cauchy's theorem in classical physics, Arch. Rational Mech. Anal., 60 (1976), pp. 305-324. | Zbl | MR

[14] M. E. Gurtin - W. O. Williams - W. Ziemer, Geometric measure theory and the axioms of continuum mechanics, Arch. Rational Mech. Anal., 92 (1985), pp. 1-22. | Zbl | MR

[15] A. Marzocchi - A. Musesti, Decomposition and integral representation of Cauchy interactions associated with measures, Continuum Mech. Thermodyn., 13 (2001), pp. 149-169. | Zbl | MR

[16] A. Marzocchi - A. Musesti, On the measure-theoretic foundations of the second law of thermodynamics, Math. Models Methods Appl. Sci., 12 (2002), pp. 721-736. | MR

[17] A. Marzocchi - A. Musesti, Balanced powers in continuum mechanics, Meccanica, 38 (2003), pp. 369-389. | Zbl | MR

[18] A. Marzocchi - A. Musesti, The Cauchy stress theorem for bodies with finite perimeter, Rend. Sem. Mat. Univ. Padova, 109 (2003), pp. 1-11. | Zbl | MR | Numdam

[19] W. Noll, The foundations of classical mechanics in the light of recent advances in continuum mechanics, in The Axiomatic Method, with Special Reference to Geometry and Physics, P. Suppes (ed). North-Holland, Amsterdam 1959 pp. 266-281. | Zbl | MR

[20] W. Noll - E. G. Virga, Fit regions and functions of bounded variation, Arch. Rational Mech. Anal., 102 (1988), pp. 1-21. | Zbl | MR

[21] G. Rodnay - R. Segev, Cauchy's flux theorem in light of the geometric integration theory, J. Elasticity, 71 (2002), pp. 183-203 Preprint, 2002. | Zbl | MR

[22] C. A. Rogers, Hausdorff measures, Cambridge, Cambridge University Press (1970). | Zbl | MR

[23] R. Segev, The geometry of Cauchy's fluxes, Arch. Rational Mech. Anal., 154 (2000), pp. 183-198. | Zbl | MR

[24] M. Sïilhavý, The existence of the flux vector and the divergence theorem for general Cauchy fluxes, Arch. Rational Mech. Anal., 90 (1985), pp. 195-212. | Zbl | MR

[25] M. Sïilhavý, Cauchy's stress theorem and tensor fields with divergences in Lp , Arch. Rational Mech. Anal., 116 (1991), pp. 223-255. | Zbl | MR

[26] R. Temam, Navier-Stokes equations, Amsterdam, North-Holland (1977). | Zbl | MR

[27] R. L. Wheeden - S. Zygmund, Measure and integral, New York and Basel, M. Dekker (1977). | Zbl | MR

[28] H. Whitney, Geometric integration theory, Princeton, Princeton University Press (1957). | Zbl | MR

[29] W. Ziemer, Cauchy flux and sets of finite perimeter, Arch. Rational Mech. Anal., 84 (1983), pp. 189-201. | Zbl | MR