Problem 2. (max. 15 points) Let F1 be a smooth vector field defined on a simply connected open subset Ul C R3. Show that Fi is both irrotational and incompressible if and only if it can be written as F1 = Vh1 for a smooth function h1 : U1 - R which satisfies Ah1 = V2h1 =0. Recall that, by A or V2, we denote the Laplace operator (in other words, the divergence of the gradient). Remark 2. Smooth functions such as the ones Problem 2 is concerned with, which satisfy the differential equation Ah = V2h =0, are called harmonic functions. Moreover, the differential equation they solve is called Laplace's equation (named after Pierre-Simon Laplace). Its solutions (that is, the harmonic functions) are a very important class of smooth functions, studied in several areas of Mathematics, such as Fourier Analysis and Stochastic Processes, as well as in Physics and Mathematical Physics