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I'm looking for a reference about existence of linear homogeneous first order PDE, in particular about the minimal assumption on the data. In literature I found that one require $C^1$-regularity on ...

Context: Let $\Omega \subset \mathbb{R}^p$ be an domain. For functions $A_{jk}^i : \Omega \to \mathbb{R}$ and $B_k^i : \Omega \to \mathbb{R}$ with some regularity, I am interested in the following ...