PDE: Elliptic form

As already noted in Chapter 2, the Poisson, Helmholtz and Laplace’s equations are the three basic examples of an elliptic type of PDE. In practice they are used to model the time-invariant response of physical systems. Without a source term the Poisson equation reduces to the Laplace’s equation whose solution, irrespective of its dimension, is referred to as a harmonic function.