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.

中文翻译：

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满足线性PDE约束的量度的尺寸估计和可纠正性

我们建立了满足线性PDE约束的措施的可纠正性。对于许多常用的PDE运算符，包括所有一阶系统和所有二阶标量运算符，获得的可整流维数是最佳的。特别是，我们的一般定理为有界变化函数（BV）和有界变形函数（BD）的可纠正性结果提供了新的证明。对于无散度张量，我们获得了多种已知结果的改进和新证明，这些结果关于可变弯度和缺陷测度的可纠正性。