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Dimensional estimates and rectifiability for measures satisfying linear PDE constraints. (arXiv:1811.01847v2 [math.AP] UPDATED)
来源于:arXiv
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. 查看全文>>