Variational Formulation of Elliptic Problems

Abstract

Poisson’s equation Δu = f is the simplest among the elliptic equations, according to the classification in Sect. 5.5, at least in dimension two. This type of equations plays an important role in the modelling of a large variety of phenomena, often of stationary nature. Typically, in drift, diffusion and reaction models like those considered in Chap. 2, a stationary solution corresponds to a steady state, with no more dependence on time.