I'm having trouble integrating $(\Delta u)^2$. If it was $\Delta u$ the primitive would just be first derivative $\nabla u.$
Any tips?
2026-03-26 21:12:39.1774559559
If $\Delta s=(\Delta u)^2$, what is $\nabla s?$
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You have Poisson's equation.
That is, $\Delta s=f$ where $f=(\Delta u)^2$.
The solution given by wiki is: $$s(\mathbf r)=-\iiint \frac{(\Delta u(\mathbf r'))^2}{4\pi\|\mathbf r - \mathbf r'\|}\,d^3\mathbf r'$$