Context: Galactic abundance gradients set strong constraints to chemo-dynamical evolutionary models of the Milky Way. Given the PL relations that provide accurate distances and the large number of spectral lines, Cepheids are excellent tracers of the present-day abundance gradients. Aims: We want to measure the Galactic abundance gradient of several chemical elements. While the slope of the Cepheid iron gradient did not vary much from the very first studies, the gradients of the other elements are not that well constrained. In this paper we focus on the inner and outer regions of the Galactic thin disk. Methods: We use HR spectra (FEROS, ESPADONS, NARVAL) to measure the abundances of several light (Na, Al), alpha (Mg, Si, S, Ca), and heavy elements (Y, Zr, La, Ce, Nd, Eu) in a sample of 65 Milky Way Cepheids. Combining these results with accurate distances from period-Wesenheit relations in the NIR enables us to determine the abundance gradients in the Milky Way. Results: Our results are in good agreement with previous studies on either Cepheids or other tracers. In particular, we confirm an upward shift of approximatively 0.2 dex for the Mg abundances, as has recently been reported. We also confirm the existence of a gradient for all the heavy elements studied in the context of a LTE analysis. However, for Y, Nd, and especially La, we find lower abundances for Cepheids in the outer disk than reported in previous studies, leading to steeper gradients. This effect can be explained by the differences in the line lists used by different groups. Conclusions: Our data do not support a flattening of the gradients in the outer disk, in agreement with recent Cepheid studies and chemo-dynamical simulations. This is in contrast to the open cluster observations but remains compatible with a picture where the transition zone between the inner disk and the outer disk would move outward with time.
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