@article{265ed62e2dab4e4f8cfa3184eb5b01e8,
title = "Dimensional estimates and rectifiability for measures satisfying linear PDE constraints",
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.",
keywords = "A-free measure, PDE constraint, Rectifiability, dimensional estimate",
author = "Adolfo Arroyo-Rabasa and {De Philippis}, Guido and Jonas Hirsch and Filip Rindler",
note = "Funding Information: This project has received funding from the European Research Council (ERC) under the European Union{\textquoteright}s Horizon 2020 research and innovation programme, Grant Agreement No. 757254 (SINGULARITY), and from the INDAM-grant “Geometric Variational Problems”. We thank the anonymous referee for various comments that improved the presentation of this paper. Funding Information: This project has received funding from the European Research Council (ERC) under the European Union?s Horizon 2020 research and innovation programme, Grant Agreement No. 757254 (SINGULARITY), and from the INDAM-grant ?Geometric Variational Problems?. We thank the anonymous referee for various comments that improved the presentation of this paper. Publisher Copyright: {\textcopyright} 2019, The Author(s).",
year = "2019",
month = jun,
day = "1",
doi = "10.1007/s00039-019-00497-1",
language = "English (US)",
volume = "29",
pages = "639--658",
journal = "Geometric and Functional Analysis",
issn = "1016-443X",
publisher = "Birkhauser Verlag Basel",
number = "3",
}