I am learning about distributions and I'm looking for an example for which the following holds:
Let $F_f(\phi):=\int_{\mathbb R^2} \phi(x)f(x)dx$ where $\phi \in C^{\infty}_0(\mathbb R^2)$ and $f$ is locally-integrable.
Find $f$ for which $-F_f(\nabla^2\phi)=\delta(\phi)$ holds, where $\delta$ is the Dirac-delta distribution
Would appreciate any help