Comparison Principle

A property for partial differential inequalities stating that an ordered pair of functions consisting of a subsolution u and a supersolution v that satisfy u ≤ v on the boundary (or at initial time) must satisfy u ≤ v throughout the domain (or for all later times). It provides a way to propagate boundary or initial inequalities into the interior by exploiting the operator's monotonicity.

A statement that if two functions satisfy an appropriate differential or integral inequality with ordered boundary or initial data, then an order relation between them holds throughout the domain; often used to deduce uniqueness, monotonicity, or bounds for PDEs.