Let $U\subset\mathbb{R}^n$ be bounded and let $f\in H^{-1}(U)$ as in \ref{def:pde-hminus1-u-2026a}. Let $u\in H_0^1(U)$ be the unique weak solution from \ref{thm:pde-poisson-weak-dirichlet-1772661803}. Then $\|\nabla u\|_{L^2(U)} \le \|f\|_{H^{-1}(U)}.$