| 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 $ |
Wikipedia: Partial differential equation