  We present directed searches for continuous gravitational waves from the
neutron stars in the Cassiopeia A (Cas A) and Vela Jr. supernova remnants. We
carry out the searches in the LIGO data from the first six months of the third
Advanced LIGO and Virgo observing run, using the Weave semi-coherent method,
which sums matched-filter detection-statistic values over many time segments
spanning the observation period. No gravitational wave signal is detected in
the search band of 20--976 Hz for assumed source ages greater than 300 years
for Cas A and greater than 700 years for Vela Jr. Estimates from simulated
continuous wave signals indicate we achieve the most sensitive results to date
across the explored parameter space volume, probing to strain magnitudes as low
as ~$6.3\times10^{-26}$ for Cas A and ~$5.6\times10^{-26}$ for Vela Jr. at
frequencies near 166 Hz at 95% efficiency.
