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The Existence of the Flux Vector and the Divergence Theorem for General Cauchy Fluxes

  • Miroslav Šilhavý

Abstract

A new proof of the existence of the flux vector is given for general Cauchy fluxes. The proof is based on an approximation theorem in the theory of functions rather than on the classical tetrahedron argument. This enables us to replace the usual assumptions of Lipschitz continuity with respect to area and volume by less restrictive assumptions so as to produce the flux vector fields with possible singularities. The classical expression for the area density of the flux is proved and the flux is shown to satisfy an appropriate version of the divergence theorem.

Keywords

Vector Field Surface Density Material Surface Borel Subset Lipschitz Continuity 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Miroslav Šilhavý
    • 1
  1. 1.Mathematical InstituteCzechoslovak Academy of SciencesPragueCzech Republic

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