Definition
Plain language
A fundamental physics equation linking a quantity to its sources, like how electric charge sets up a field, used as a test problem.
As stated in the literature
A second-order elliptic PDE relating a field's Laplacian to a source term, ubiquitous in electrostatics and fluid pressure; a standard benchmark in physics-informed machine learning.
Why it matters: It appears across physics from electricity to fluid pressure, making it a go-to test problem for simulation methods.
For example, it describes how a fixed pattern of electric charges sets up the electric field that fills the space around them.