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arXiv · 1811.01847

Dimensional estimates and rectifiability for measures satisfying linear PDE constraints

Adolfo Arroyo-Rabasa·Guido De Philippis·Jonas Hirsch·Filip Rindler
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Abstract

We establish the rectifiability of measures satisfying a linear PDE constraint. The obtained rectifiability dimensions are optimal for many usual PDE operators, including all first-order systems and all second-order scalar operators. In particular, our general theorem provides a new proof of the rectifiability results for functions of bounded variations (BV) and functions of bounded deformation (BD). For divergence-free tensors we obtain refinements and new proofs of several known results on the rectifiability of varifolds and defect measures.

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Adolfo Arroyo-Rabasa, Guido De Philippis, Jonas Hirsch, Filip Rindler. 2018-11-05. Dimensional estimates and rectifiability for measures satisfying linear PDE constraints. https://arxiv.org/abs/1811.01847

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