Calculus of Variations and Geometric Measure Theory
home | mail | papers | authors | news | seminars | events | open positions | login

A. Arroyo-Rabasa - G. De Philippis - J. Hirsch - F. Rindler

Dimensional estimates and rectifiability for measures satisfying linear PDE constraints

created by dephilipp on 06 Nov 2018

[BibTeX]

Submitted Paper

Inserted: 6 nov 2018
Last Updated: 6 nov 2018

Year: 2018

ArXiv: 1811.01847 PDF

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 and all second-order operators). Our general theorem provides a new proof of the rectifiability results for functions of bounded variations and functions of bounded deformation. For divergence-free tensors we obtain refinements and new proofs of several known results on the rectifiability of varifolds and defect measures.


Download:

Credits | Cookie policy | HTML 5 | CSS 2.1