Dirichlet problem and problems on uniform approximation for solutions of elliptic equations with constant complex coefficients.

In the talk we plan to consider the problem of uniform approximation of functions by solutions of homogeneous elliptic equations with constant complex coefficients on compact sets in the complex plane. We give a survey on classical and recent results concerning the matter, and then we state and discuss some open problems. Furthermore, we are going to discuss the Dirichlet problem for solutions of such equations and its connection with the aforesaid approximation problem.