Suppose we have a compact plane region $R$ (not necessarily convex or connected). I am working in a problem which involves the point $p$ in $R$ that is, in average, the closest to every other point. That is, the point in $R$ which minimizes $$\int_R d(p,x) dx.$$ I have been looking for references but I can't find this point anywhere (it is certainly not the centroid / baricenter, as the centroid doesn't even need to be a point in $R$).

Do you know if this point has a name or has been studied previously?