Solution
= Solution
Write the <elliptic differential operator> as $L=\Delta+r\partial_x+s\partial_y$. At an interior maximum, $u_x=u_y=0$ and $u_{xx}+u_{yy}\leq0$. Therefore $Lu\leq0$ there, contradicting $Lu=f>0$.
The <extreme value theorem> ensures that a maximum exists on the compact closed disk. It cannot lie in the interior, so \b[the maximum is attained on $\partial D$]. The drift terms disappear at a stationary point, which is why the strict-sign proof is so short.