Large $\mathrm{\mid }k\mathrm{\mid }$ behavior of d-bar problems for domains with a smooth boundary

In a previous work on the large $\mathrm{\mid }k\mathrm{\mid }$ behavior of complex geometric optics solutions to a system of d-bar equations, we treated in detail the situation when a certain potential is the characteristic function of a strictly convex set with real-analytic boundary. We here extend the results to the case of sets with smooth boundary, by using almost holomorphic functions.