$\phi(x)$ is harmonic in $C^2$
in proof for solution of poisson's equation($- \Delta u=f$) ,this step came it maybe very fundamental but I am not getting it
$u(x)= \int_{R^n}\phi(x-y)f(y)\mathrm dy = \int_{R^n}\phi(x)f(x-y)\mathrm dy$
how this transformation happened without negative sign?
and this step?
$\int_{B(0,\epsilon)}\phi(y)\Delta_xf(x-y)\mathrm dy \leq C||D^2f||_{L^{\infty}(R^n)}\int_{B(0,\epsilon)}|\phi(y)|\mathrm dy \leq C\epsilon^2|log \epsilon| for (n=2),C\epsilon^2 for (n\geq3) $
$\int_{R^n-B(0,\epsilon)}\phi(y)\Delta_xf(x-y)\mathrm dy \leq ||Df||_{L^{\infty}(R^n)}\int_{\partial B(0,\epsilon)}|\phi(y)|\mathrm dSy \leq C\epsilon|log \epsilon| for (n=2),C\epsilon for (n\geq3) $
