Just under equation 3.40 in the book The Boundary Element Method for Engineers and Scientists (Second Edition) by John T. Katsikadelis, in the context of solving a Poisson Equation
$\nabla^2 u(P) = f(P)$, as the author wants to show that
$$u = \int_{\Omega} v f d\Omega$$, where $v$ is the fundamental solution.
Using $\nabla^2 u(P) = f(P) = \int_\Omega \delta(Q - P) f(Q) d\Omega_Q$
He shows the following equation, where he pulls out the laplacian ($\nabla^2$) out of the integral. I would like to understand whether it's true in general or why he can pull it out in this context if not.
$$\nabla^2 u(P) = \int_{\Omega} \nabla^2v(Q, P) f(Q) d\Omega_Q = \nabla^2 \left[ \int_{\Omega} v(Q, P) f(Q) d\Omega_Q\right]$$
Where the subscript is the variable that changes.