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

@inproceedings{Chen2008GaussGreenTF,
  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},
  year={2008}
}
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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