I am wondering if there is a physical interpretation of the Laplace operator (also known as Laplacian, Δ, ∇2, or ∇·∇). From my impression a gradient of a function is the vector field in the direction with the greatest change. Also a divergence is volume density of flux from a point source. Can I think of the Laplacian as the volume density of the flux in direction of greatest change from a point source? I am trying to use the identity that the Laplace operator is the divergence of the gradient. I am not sure what I am proposing makes sense. I am a new student to vector calculus so I am trying to understand the physical meaning of these terms. Please correct me if anything that I have stated is incorrect. Thanks.