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Some fine properties of currents and applications to distributional Jacobians. (English) Zbl 1025.49029
The author studies the fine properties of currents in the framework of geometric measure theory on metric spaces developed by L. Ambrosio and B. Kirchheim [Acta Math. 185, No. 1, 1-80 (2000; Zbl 0984.49025)], and he proves a rectifiability criterion for flat currents of finite mass. The structure of the distributional Jacobians of functions in the space BnV is investigated: the author introduces the subspace of special functions of bounded higher variation, and he proves a closure theorem.

MSC:
49Q20 Variational problems in a geometric measure-theoretic setting
49Q15 Geometric measure and integration theory, integral and normal currents in optimization
49J10 Existence theories for free problems in two or more independent variables
Citations:
Zbl 0984.49025
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