Dimensional estimates and rectifiability for measures satisfying linear PDE constraints

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 rec...

Full description

Saved in:
Bibliographic Details
Published inGeometric and functional analysis Vol. 29; no. 3; pp. 639 - 658
Main Authors Arroyo-Rabasa, Adolfo, De Philippis, Guido, Hirsch, Jonas, Rindler, Filip
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2019
Springer Nature B.V
Subjects
Analysis
Deformation
Divergence
Mathematics
Mathematics and Statistics
Operators
Tensors
dimensional estimate
Rectifiability
free measure
PDE constraint
Online AccessGet full text

Cover

More Information
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-019-00497-1