  Young core-collapse supernovae with dense-wind progenitors may be able to
accelerate cosmic-ray hadrons beyond the knee of the cosmic-ray spectrum, and
this may result in measurable gamma-ray emission. We searched for gamma-ray
emission from ten supernovae observed with the High Energy Stereoscopic System
(H.E.S.S.) within a year of the supernova event. Nine supernovae were observed
serendipitously in the H.E.S.S. data collected between December 2003 and
December 2014, with exposure times ranging from 1.4 hours to 53 hours. In
addition we observed SN 2016adj as a target of opportunity in February 2016 for
13 hours. No significant gamma-ray emission has been detected for any of the
objects, and upper limits on the $>1$ TeV gamma-ray flux of the order of
$\sim$10$^{-13}$ cm$^{-2}$s$^{-1}$ are established, corresponding to upper
limits on the luminosities in the range $\sim$2 $\times$ 10$^{39}$ erg s$^{-1}$
to $\sim$1 $\times$ 10$^{42}$ erg s$^{-1}$. These values are used to place
model-dependent constraints on the mass-loss rates of the progenitor stars,
implying upper limits between $\sim$2 $\times 10^{-5}$ and $\sim$2 $\times
10^{-3}$M$_{\odot}$yr$^{-1}$ under reasonable assumptions on the particle
acceleration parameters.
