Gauss-Green Theorem for Weakly Differentiable Vector Fields , Sets of Finite Perimeter , and Balance Laws

  title={Gauss-Green Theorem for Weakly Differentiable Vector Fields , Sets of Finite Perimeter , and Balance Laws},
  author={Gui-Qiang G. Chen and Monica Torres and William P. Ziemer},
We analyze a class of weakly differentiable vector fields F W RN ! RN with the property that F 2 L1 and div F is a (signed) Radon measure. These fields are called bounded divergence-measure fields. The primary focus of our investigation is to introduce a suitable notion of the normal trace of any divergencemeasure field F over the boundary of an arbitrary set of finite perimeter that ensures the validity of the Gauss-Green theorem. To achieve this, we first establish a fundamental approximation… CONTINUE READING
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Publications referenced by this paper.
Showing 1-10 of 58 references

Divergence measure fields and Cauchy’s stress theorem

  • M. Šilhavý
  • Rend. Sem. Mat. Univ. Padova
  • 2005
Highly Influential
7 Excerpts

Divergence-measure fields, sets of finite perimeter, and conservation laws

  • G.-Q. Chen, M. Torres
  • Arch. Ration. Mech. Anal
  • 2005
Highly Influential
10 Excerpts

Hyperbolic systems of conservation laws with a symmetry

  • G. Q. Chen
  • Comm. Partial Differential Equations
  • 1991
Highly Influential
18 Excerpts

On the equation divY D f and application to control of phases

  • J. Bourgain, H. Brezis
  • J. Amer. Math. Soc
  • 2003
Highly Influential
4 Excerpts

Cauchy fluxes associated with tensor fields having divergence measure

  • M. Degiovanni, A. Marzocchi, A. Musesti
  • Arch. Ration. Mech. Anal
  • 1999
Highly Influential
3 Excerpts

Cauchy flux and sets of finite perimeter

  • W. P. Ziemer
  • Arch. Rational Mech. Anal
  • 1983
Highly Influential
17 Excerpts

Complementi alla teoria della misura .n 1/-dimensionale in uno spazio ndimensionale

  • E. De Giorgi
  • Seminario di Matematica della Scuola Normale…
  • 1960
Highly Influential
17 Excerpts

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