A. Arroyo-Rabasa - G. De Philippis - J. Hirsch - F. Rindler
Dimensional estimates and rectifiability for measures satisfying linear PDE constraints
Accepted Paper
Inserted: 6 nov 2018
Last Updated: 31 jan 2019
Journal: Geom. Funct. Anal.
Year: 2018
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 and all second-order operators). Our general theorem provides a new proof of the rectifiability results for functions of bounded variations and functions of bounded deformation. 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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