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Dimensional estimates and rectifiability for measures satisfying linear PDE constraints
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Arroyo-Rabasa, Adolfo, De Philippis, Guido, Hirsch, Jonas and Rindler, Filip (2019) Dimensional estimates and rectifiability for measures satisfying linear PDE constraints. Geometric and Functional Analysis, 29 (3). pp. 639-658. doi:10.1007/s00039-019-00497-1 ISSN 1016-443X.
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Official URL: https://doi.org/10.1007/s00039-019-00497-1
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.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Journal or Publication Title: | Geometric and Functional Analysis | ||||||||
Publisher: | Springer International Publishing | ||||||||
ISSN: | 1016-443X | ||||||||
Official Date: | June 2019 | ||||||||
Dates: |
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Volume: | 29 | ||||||||
Number: | 3 | ||||||||
Page Range: | pp. 639-658 | ||||||||
DOI: | 10.1007/s00039-019-00497-1 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 4 February 2019 | ||||||||
Date of first compliant Open Access: | 30 August 2019 | ||||||||
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