PDE system

context	$D,d,n,m,k\in\mathbb N$
context	$\alpha$ … sequence of length $n$ of multi-indices
context	$F:\mathbb R^D\times\mathbb R^{d\ \cdot\ (1+n)}\to \mathbb R^m$
definiendum	$u \in \mathrm{it}$
postulate	$u:C^k(\mathbb R^D,\mathbb R^d)$
postulate	$F(x,u(x),u^{(\alpha_1)}(x),u^{(\alpha_2)}(x),\dots,u^{(\alpha_n)}(x))=0$