Dimensional estimates and rectifiability for measures satisfying linear PDE constraints
Analysis of PDEs
2019-02-01 v2 Functional Analysis
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.
Cite
@article{arxiv.1811.01847,
title = {Dimensional estimates and rectifiability for measures satisfying linear PDE constraints},
author = {Adolfo Arroyo-Rabasa and Guido De Philippis and Jonas Hirsch and Filip Rindler},
journal= {arXiv preprint arXiv:1811.01847},
year = {2019}
}
Comments
17 pages; to appear in GAFA