Critical weak-$L^p$ differentiability of singular integrals

Luigi Ambrosio, Augusto C. Ponce, Rémy Rodiac

We establish that for every function $u\in L_{\mathrm{loc}}^1(\Omega )$ whose distributional Laplacian $\Delta u$ is a signed Borel measure in an open set $\Omega$ in ${\mathbb{R}}^N$, the distribut…