For classical solutions, we saw in the previous chapter that we can go from a problem with second-order derivatives to a variational formulation with just first-order derivatives. By using the generalized integration-by-parts formulae, now we will justify this transition to the lower order derivatives in the general case. Once that is done, we will solve variational formulations that are defined in Sobolev spaces, allowing us to establish the existence and uniqueness of solutions to the Dirichlet, Neumann and Fourier problems. We place ourselves in Ω, an open set of ℝd whose boundary is Lipschitz and bounded.