This is called Poisson's equation, a generalization of Laplace's equation.Laplace's equation and Poisson's equation are the simplest examples of elliptic partial differential equations.Laplace's equation is also a special case of the Helmholtz equation.. The general theory of solutions to Laplace's equation is known as potential theory.The twice continuously differentiable solutions …

In physics, the Young–Laplace equation (/ l ə ˈ p l ɑː s /) is a nonlinear partial differential equation that describes the capillary pressure difference sustained across the interface between two static fluids, such as water and air, due to the phenomenon of surface tension or wall tension, although use of the latter is only applicable if assuming that the wall is very thin.

Jun 17, 2017 · Because Laplace's equation is a linear PDE, we can use the technique of separation of variables in order to convert the PDE into several ordinary differential equations (ODEs) that are easier to solve. Linearity ensures that the solution set consists of …