Abstract: We study elliptic partial differential operators in divergence form on open sets in R^n and associated with complex uniformly strictly accretive matrices. We present several results for such operators, the central being the so-called bilinear embedding theorem. The proof of this theorem is a combination of heat flows and Bellman functions, and leads to a new concept of convexity of power functions |z|^p for complex z and associated with accretive matrices. This concept turns out to be a generalization of the classical ellipticity condition and seems to be well suited for the study of elliptic PDE on L^p spaces. The talk is based on collaboration with Andrea Carbonaro (U. Genova).