We performed sub-arcsecond high-sensitivity nterferometric 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 about 60 AU at the Taurus distance. We report the existence of a cavity of about 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 about 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. 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 about 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 a too simplistic 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 to determine the dust emissivity index.