I am wondering what does $\Delta_x \Phi(x-y)$ really mean? I come cross the claim that $\Delta_x \Phi(x-y)=\Delta_y \Phi(x-y)$. I am hoping anyone could help me explain that.
2026-04-01 09:57:00.1775037420
laplacian equation notation Evans
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We can write $$ \Delta_x \Phi(x-y)=\Delta \Phi(\cdot-y)(x) $$ or $$ \Delta_x \Phi(x-y)=\Delta F(x) , $$ where $$ F(x) = \Phi(x-y) . $$