  Brown dwarf disks are excellent laboratories to test our understanding of
disk physics in an extreme parameter regime. In this paper we investigate a
sample of 29 well-characterized brown dwarfs and very low mass stars, for which
Herschel far-infrared fluxes as well as (sub)-mm fluxes are available. We have
measured new Herschel PACS fluxes for 11 objects and complement these with
(sub)-mm data and Herschel fluxes from the literature. We analyze their
spectral energy distributions in comparison with results from radiative
transfer modeling. Fluxes in the far-infrared are strongly affected by the
shape and temperature of the disk (and hence stellar luminosity), whereas the
(sub)-mm fluxes mostly depend on disk mass. Nevertheless, there is a clear
correlation between far-infrared and (sub)-mm fluxes. We argue that the link
results from the combination of the stellar mass-luminosity relation and a
scaling between disk mass and stellar mass. We find strong evidence of dust
settling to the disk midplane. The spectral slopes between near- and
far-infrared are mostly between $-0.5$ and $-1.2$ in our sample, comparable to
more massive T Tauri stars, which may imply that the disk shapes are similar as
well, though highly-flared disks are rare among brown dwarfs. We find that dust
temperatures in the range of 7-15 K, calculated with
$T\approx25\,(L/L_\odot)^{0.25}$ K, are appropriate for deriving disk masses
from (sub)-mm fluxes for these low luminosity objects. About half of our sample
hosts disks with at least one Jupiter mass, confirming that many brown dwarfs
harbour sufficient material for the formation of Earth-mass planets in their
midst.
