Let $\Omega$ be an 2D interval and let $\omega_1, ..., \omega_n$ a set points in $\Omega$. I am looking for that set points $\omega_1, ..., \omega_n$ such that following integral is minimized $$\int_\Omega \min_{i = 1,...,n} |x-\omega_i| \mathrm{d} x$$
Can someone help me finding this?
Many thanks, Koen