Dimensional estimates and rectifiability for measures satisfying linear PDE constraints

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

doi:10.1007/s00039-019-00497-1

Dimensional estimates and rectifiability for measures satisfying linear PDE constraints

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

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	639-658
Number of pages	20
Journal	Geometric and Functional Analysis
Volume	29
Issue number	3
DOIs	https://doi.org/10.1007/s00039-019-00497-1
State	Published - Jun 1 2019

Keywords

A-free measure
PDE constraint
Rectifiability
dimensional estimate

ASJC Scopus subject areas

Analysis
Geometry and Topology

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10.1007/s00039-019-00497-1

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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.",

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author = "Adolfo Arroyo-Rabasa and {De Philippis}, Guido and Jonas Hirsch and Filip Rindler",

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T1 - Dimensional estimates and rectifiability for measures satisfying linear PDE constraints

AU - Arroyo-Rabasa, Adolfo

AU - De Philippis, Guido

AU - Hirsch, Jonas

AU - Rindler, Filip

PY - 2019/6/1

Y1 - 2019/6/1

N2 - 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.

AB - 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.

KW - A-free measure

KW - PDE constraint

KW - Rectifiability

KW - dimensional estimate

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JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 3

ER -

Dimensional estimates and rectifiability for measures satisfying linear PDE constraints

Abstract

Keywords

ASJC Scopus subject areas

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