Dimensional estimates and rectifiability for measures satisfying linear PDE constraints

Adolfo Arroyo-Rabasa, Guido De Philippis, Jonas Hirsch, Filip Rindler

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)639-658
Number of pages20
JournalGeometric and Functional Analysis
Issue number3
StatePublished - Jun 1 2019


  • A-free measure
  • PDE constraint
  • Rectifiability
  • dimensional estimate

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology


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