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

All suggestions all welcome.