  Spinning neutron stars asymmetric with respect to their rotation axis are
potential sources of continuous gravitational waves for ground-based
interferometric detectors. In the case of known pulsars a fully coherent
search, based on matched filtering, which uses the position and rotational
parameters obtained from electromagnetic observations, can be carried out.
Matched filtering maximizes the signal-to-noise (SNR) ratio, but a large
sensitivity loss is expected in case of even a very small mismatch between the
assumed and the true signal parameters. For this reason, {\it narrow-band}
analyses methods have been developed, allowing a fully coherent search for
gravitational waves from known pulsars over a fraction of a hertz and several
spin-down values. In this paper we describe a narrow-band search of eleven
pulsars using data from Advanced LIGO's first observing run. Although we have
found several initial outliers, further studies show no significant evidence
for the presence of a gravitational wave signal. Finally, we have placed upper
limits on the signal strain amplitude lower than the spin-down limit for 5 of
the 11 targets over the bands searched: in the case of J1813-1749 the spin-down
limit has been beaten for the first time. For an additional 3 targets, the
median upper limit across the search bands is below the spin-down limit. This
is the most sensitive narrow-band search for continuous gravitational waves
carried out so far.
