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Dimensional estimates and rectifiability for measures satisfying linear PDE constraints

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arxiv 1811.01847 v2 pith:ZXDECZUS submitted 2018-11-05 math.AP math.FA

Adolfo Arroyo-Rabasa , Guido De Philippis , Jonas Hirsch , Filip Rindler This is my paper
classification math.APmath.FA
keywords rectifiabilitymeasuresboundedfunctionslinearoperatorsresultssatisfying
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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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