Photoevaporation due to high-energy stellar photons is thought to be one of the main drivers of protoplanetary disk dispersal. The fully or partially ionized disk surface is expected to produce free-free continuum emission at centimeter (cm) wavelengths that can be routinely detected with interferometers such as the upgraded Very Large Array (VLA). We use deep (rms noise down to 8 $mu$Jy beam$^{-1}$ in the field of view center) 3.5 cm maps of the nearby (130 pc) Corona Australis (CrA) star formation (SF) region to constrain disk photoevaporation models. We find that the radio emission from disk sources in CrA is surprisingly faint. Only 3 out of 10 sources within the field of view are detected, with flux densities of order $10^2$ $mu$Jy. However, a significant fraction of their emission is non-thermal. Typical upper limits for non-detections are $3sigmasim 60~mu$Jy beam$^{-1}$. Assuming analytic expressions for the free-free emission from extreme-UV (EUV) irradiation, we derive stringent upper limits to the ionizing photon luminosity impinging on the disk surface $Phi_mathrm{EUV}<1-4times10^{41}$ s$^{-1}$. These limits constrain $Phi_mathrm{EUV}$ to the low end of the values needed by EUV-driven photoevaporation models to clear protoplanetary disks in the observed few Myr timescale. Therefore, at least in CrA, EUV-driven photoevaporation is not likely to be the main agent of disk dispersal. We also compare the observed X-ray luminosities $L_X$ of disk sources with models in which photoevaporation is driven by such photons. Although predictions are less specific than for the EUV case, most of the observed fluxes (upper limits) are roughly consistent with the (scaled) predictions. Deeper observations, as well as predictions spanning a wider parameter space, are needed to properly test X-ray driven photoevaporation.
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