We prove a Lusin type theorem for a certain class of linear partial differential operators G(D), reducing to [1, Theorem 1] when G(D) is the gradient. Moreover, we describe the structure of the set {G(D)f = F}, under assumptions of non-integrability on F, in terms of lower dimensional rectifiability and superdensity. Applications to Maxwell type system and to multivariable Cauchy–Riemann system are provided.

中文翻译：

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线性偏微分算子 G(D) 的恒等式 G(D)f = F。Lusin 类型和结构导致不可积情况

我们证明了某类线性偏微分算子的 Lusin 型定理G(D)，减少到 [1, Theorem 1] 当G(D) 是梯度。此外，我们描述了集合的结构{G(D)F=F}，在不可积性的假设下F，就低维可整流性和超密度而言。提供了对麦克斯韦型系统和多变量柯西-黎曼系统的应用。