Suppose I have a long algebraic expression, and in there somewhere I have derivatives of a function V[x,y,z].

I want to set

D[V[x,y,z], {x,2}] + D[V[x,y,z], {y,2}] + D[V[x,y,z], {z,2}] 

to zero. How can I program this? I don't want to specify the function, I just want to set its Laplacian to zero.