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On the structure of 𝓐-free measures and applications
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Journal Article
On the structure of 𝓐-free measures and applications
2016
Overview
We establish a general structure theorem for the singular part of 𝓐-free Radon measures, where 𝓐 is a linear PDE operator. By applying the theorem to suitably chosen differential operators 𝓐, we obtain a simple proof of Alberti's rank-one theorem and, for the first time, its extensions to functions of bounded deformation (BD). We also prove a structure theorem for the singular part of a finite family of normal currents. The latter result implies that the Rademacher theorem on the differentiability of Lipschitz functions can hold only for absolutely continuous measures and that every top-dimensional Ambrosio-Kirchheim metric current in ℝd is a Federer-Fleming flat chain.
Publisher
Department of Mathematics at Princeton University,Princeton University, Department of Mathematics
