A Green's function is a fundamental solution that also satisfies a suitable condition on the boundary S of a volume V. For instance, G ( x , y , z ; x ′ , y ′ , z ′ ) may satisfy ∇ ∇ ⋅ ⋅ ∇ ∇ G = − − δ δ ( x − − x ′ , y − − y ′ , z − − z ′ ) in V , G = 0 if ( x , y , z ) on S .