Calculus of Variations and Geometric Measure Theory

A. Arroyo-Rabasa - G. De Philippis - J. Hirsch - F. Rindler

Dimensional estimates and rectifiability for measures satisfying linear PDE constraints

created by dephilipp on 06 Nov 2018
modified on 31 Jan 2019


Accepted Paper

Inserted: 6 nov 2018
Last Updated: 31 jan 2019

Journal: Geom. Funct. Anal.
Year: 2018

ArXiv: 1811.01847 PDF


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.