Minimum of a quartic over a half plane

Consider the domain $D=\{(x,y)\in\mathbb R^2:x\le y\}$ and the function $h:D\to\mathbb R$ defined by

$$h\big((x,y)\big)=(x-2)^4+(y-1)^4,\quad(x,y)\in D.$$

Then the minimum value of $h$ on $D$ equals