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A descriptive definition of a variational integral and applications. (English) Zbl 0747.26010

The author has introduced a coordinate free variational integral on bounded sets of finite perimeter, for which a Gauss-Green theorem holds for continuous vector fields which are differentiable outside a set whose codimension one Hausdorff dimension is \(\sigma\)-finite. This paper proposes a descriptive definition of this integral which allows an extension of the result to vector fields which are discontinuous on a set of positive Lebesgue measure. The proof makes use of interesting properties of BV sets. The results are compared to earlier ones of Shapiro and Jurkat.

MSC:

26B20 Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.)
26B15 Integration of real functions of several variables: length, area, volume
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