  Aims: The iron abundance gradient in the Galactic stellar disk provides
fundamental constraints on the chemical evolution of this important Galaxy
component. However the spread around the mean slope is, at fixed Galactocentric
distance, larger than estimated uncertainties. Methods: To provide quantitative
constraints on these trends we adopted iron abundances for 265 classical
Cepheids (more than 50% of the currently known sample) based either on
high-resolution spectra or on photometric metallicity indices. Homogeneous
distances were estimated using near-infrared Period-Luminosity relations. The
sample covers the four disk quadrants and their Galactocentric distances range
from ~5 to ~17 kpc. Results: A linear regression over the entire sample
provides an iron gradient of -0.051+/-0.004 dex/kpc. The above slope agrees
quite well, within the errors, with previous estimates based either on Cepheids
or on open clusters covering similar Galactocentric distances. However, once we
split the sample in inner (Rg < 8 kpc) and outer disk Cepheids we found that
the slope (-0.130+/-0.015 dex/kpc) in the former region is ~3 times steeper
than the slope in the latter one (-0.042+/-0.004 dex/kpc). We found that in the
outer disk the radial distribution of metal-poor (MP, [Fe/H]<-0.02 dex) and
metal-rich (MR) Cepheids across the four disk quadrants does not show a clear
trend when moving from the innermost to the external disk regions. We also
found that the relative fractions of MP and MR Cepheids in the 1st and in the
3rd quadrant differ at 8 sigma (MP) and 15 sigma (MR) level.
