The integral version of Gauss's equation can thus be rewritten as ∭ ∭ Ω Ω ( ∇ ∇ ⋅ ⋅ E − − ρ ρ ε ε 0 ) d V = 0 Since Ω is arbitrary (e.g. an arbitrary small ball with arbitrary center), this is satisfied if and only if the integrand is zero everywhere. This is the differential equations formulation of Gauss equation up to a trivial rearrangement.