PDE system

Set

 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 $F(x,u(x),u^{(\alpha_1)}(x),u^{(\alpha_2)}(x),\dots,u^{(\alpha_n)}(x))=0$