>>531
∂f/∂x=g'(r)(∂r/∂x)=g'(r)(x/r)
∂^2f/∂x^2=g''(r)(x/r)^2+g'(r){1/r-(x/r^2)(∂r/∂x)}=g''(r)(x/r)^2+g'(r){1/r-(x^2/r^3)}

∂^2f/∂x^2+∂^2f/∂y^2+∂^2f/∂z^2
=g''(r){(x/r)^2+(y/r)^2+(z/r)^2}+g'(r){3/r-(x^2+y^2+z^2)/r^3}
=g''(r)+g'(r)(2/r)
=0 とおくと

{r^2g'(r)}'=0
r^2g'(r)=-a
g'(r)=-a/r^2
g(r)=a/r+b