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.

Dimensional estimates and rectifiability for measures satisfying linear PDE constraints / Arroyo-Rabasa, A.; De Philippis, G.; Hirsch, J.; Rindler, F.. - In: GEOMETRIC AND FUNCTIONAL ANALYSIS. - ISSN 1016-443X. - 29:(2019), pp. 639-658. [10.1007/s00039-019-00497-1]

Dimensional estimates and rectifiability for measures satisfying linear PDE constraints

De Philippis, G.;
2019-01-01

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.
2019
29
639
658
https://arxiv.org/abs/1811.01847
Arroyo-Rabasa, A.; De Philippis, G.; Hirsch, J.; Rindler, F.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/118187
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