Consider the following second-order linear partial differential equation (PDE) in two variables:

Au_xx + Bu_xy + Cu_yy + Du _x + Eu_y + Fu = G(x,y) -----(Eqn 1)

Where, A, B, C, D, E, F and G can be constants or functions of x and y.

The above PDE (Eqn 1) is elliptic if B² - 4AC < 0. Elliptic PDE describe steady-state phenomena.