Aims.We constrain the dust distribution and its properties (temperature, emissivity) in inner proto-planetary disks Methods: .We performed sub-arcsecond high-sensitivity interferometric observations of the thermal dust emission at 1.4 mm and 2.8 mm in the disks surrounding LkCa 15 and MWC 480, with the new 750 m baselines of the IRAM PdBI array. This provides a linear resolution of ~60 AU at the distance of Taurus. Results: .We report the existence of a cavity of ~50 AU radius in the inner disk of LkCa 15. Whereas LkCa 15 emission is optically thin, the optically thick core of MWC 480 is resolved at 1.4 mm with a radius of ~35 AU, constraining the dust temperature. In MWC 480, the dust emission is coming from a colder layer than the CO emission, most likely the disk mid-plane. Conclusions: .These observations provide direct evidence of an inner cavity around LkCa 15. Such a cavity most probably results from the tidal disturbance created by a low-mass companion or large planet at ~30 AU from the star. These results suggest that planetary system formation is already at work in LkCa 15. They also indicate that the classical steady-state viscous disk model is too simplistic a description of the inner 50 AU of "proto-planetary" disks and that the disk evolution is coupled to the planet formation process. The MWC 480 results indicate that a proper estimate of the dust temperature and size of the optically thick core are essential for determining the dust emissivity index ?.Read less <