  Context. High-precision pulsar-timing experiments are affected by temporal
variations of the Dispersion Measure (DM), which are related to spatial
variations in the interstellar electron content. Correcting for DM variations
relies on the cold-plasma dispersion law which states that the dispersive delay
varies with the squared inverse of the observing frequency. This may however
give incorrect measurements if the probed electron content (and therefore the
DM) varies with observing frequency, as is predicted theoretically.
  Aims. We study small-scale density variations in the ionised interstellar
medium. These structures may lead to frequency-dependent DMs in pulsar signals
and could inhibit the use of lower-frequency pulsar observations to correct
time-variable interstellar dispersion in higher-frequency pulsar-timing data.
  Methods. We used high-cadence, low-frequency observations with three stations
from the German LOng-Wavelength (GLOW) consortium, which are part of the LOw
Frequency ARray (LOFAR). Specifically, 3.5 years of weekly observations of PSR
J2219+4754 are presented.
  Results. We present the first detection of frequency-dependent DMs towards
any interstellar object and a precise multi-year time-series of the time- and
frequency-dependence of the measured DMs. The observed DM variability is
significant and may be caused by extreme scattering events. Potential causes
for frequency-dependent DMs are quantified and evaluated.
  Conclusions. We conclude that frequency-dependence of DMs has been reliably
detected and is caused by small-scale (up to 10s of AUs) but steep density
variations in the interstellar electron content. We find that long-term trends
in DM variability equally affect DMs measured at both ends of our frequency
band and hence the negative impact on long-term high-precision timing projects
is expected to be limited.
