Divergence measure fields and Cauchy's stress theorem
Rendiconti del Seminario Matematico della Università di Padova, Tome 113 (2005), pp. 15-45. 
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     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},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {113},
     year = {2005},
     mrnumber = {2168979},
     zbl = {1167.74317},
     language = {en},
     url = {http://archive.numdam.org/item/RSMUP_2005__113__15_0/}
}
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Silhavy, Miroslav. Divergence measure fields and Cauchy's stress theorem. Rendiconti del Seminario Matematico della Università di Padova, Tome 113 (2005), pp. 15-45. http://archive.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. | MR | Zbl

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

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

[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. | MR | Zbl

[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. | MR | Zbl

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

[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. | MR | Zbl

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

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

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

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

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

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

[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. | MR | Zbl

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

[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. | MR | Zbl

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

[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. | MR | Zbl

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

[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. | MR | Zbl

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

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

[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. | MR | Zbl

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

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

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

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

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