Elliptic Systems in Divergence Form

In this chapter, we take a first look at complex elliptic systems in divergence form. This will be based on the variational approach using the Lax–Milgram lemma. Later, in Chap. 12 , we will recover these definitions in the context of first-order formulations and extend them to a larger class of perturbed systems. Both perspectives are natural, and it will be useful to have both of them at our disposal.