  The main goal of this paper is to provide new insights on the origin of the
observable flux of gamma rays from HESS J1809-193 using new high-quality
observations in the radio domain. We used the Expanded Very Large Array (now
known as the Karl G. Jansky Very large Array, JVLA) to produce a deep
full-synthesis imaging at 1.4 GHz of the vicinity of PSR J1809-1917. These data
were used in conjunction with 12CO observations from the James Clerk Maxwell
Telescope in the transition line J=3-2 and atomic hydrogen data from the
Southern Galactic Plane Survey to investigate the properties of the
interstellar medium in the direction of the source HESS J1809-193. The new
radio continuum image, obtained with a synthesized beam of 8"x4" and a
sensitivity of 0.17 mJy/beam, reveals with unprecedented detail all the
intensity structures in the field. No radio counterpart to the observed X-ray
emission supposed to be a pulsar wind nebula powered by PSR J1809-1917 is seen
in the new JVLA image. We discovered a system of molecular clouds on the edge
of the supernova remnant (SNR) G11.0-0.0 shock front, which is positionally
coincident with the brightest part of the TeV source HESS J1809-193. We
determine, on the basis of kinematic and morphological evidences, a physical
link of the SNR with the clouds for which we estimated a total (molecular plus
atomic) mass of ~3 x10^3 Mo and a total proton density in the range 2-3 x 10^3
cm-3. We propose as the most likely origin of the very high-energy gamma-ray
radiation from HESS J1809-193 a hadronic mechanism through collisions of ions
accelerated at the SNR G11.0-0.0 shock with the molecular matter in the
vicinity of the remnant.
